%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP156^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:55 AM UTC 2026
% Result : Theorem 5.62s 1.13s
% Output : Refutation 5.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP156^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 20:03:35 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.62/1.13 % (1523161)Will run a generic schedule for satisfiability detection.
% 5.62/1.13 % (1523167)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3919350031_2999 on theBenchmark for (2999ds/0Mi)
% 5.62/1.13 % (1523168)% WARNING: option uhcvi not known.
% 5.62/1.13 % (1523168)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2106663611:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.62/1.13 % (1523169)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2764474290:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.62/1.13 % (1523170)dis+10_1_sil=32000:sp=arity:random_seed=3486862649:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.62/1.13 % (1523171)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=982418231:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523168)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.62/1.13 % (1523173)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2403286776:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.62/1.13 % (1523172)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3462125493:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.62/1.13 % (1523171)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.62/1.13 % (1523179)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1693013163:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 5.62/1.13 % (1523168)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.62/1.13 % (1523170)Instruction limit reached!
% 5.62/1.13 % (1523170)------------------------------
% 5.62/1.13 % (1523170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523170)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523170)Termination reason: Instruction limit
% 5.62/1.13 % (1523170)Termination phase: Saturation
% 5.62/1.13 % (1523170)Time elapsed: 0.045 s
% 5.62/1.13 % (1523170)Peak memory usage: 13 MB
% 5.62/1.13 % (1523170)Instructions burned: 104 (million)
% 5.62/1.13 % (1523173)Instruction limit reached!
% 5.62/1.13 % (1523173)------------------------------
% 5.62/1.13 % (1523173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523173)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523173)Termination reason: Instruction limit
% 5.62/1.13 % (1523173)Termination phase: Saturation
% 5.62/1.13 % (1523173)Time elapsed: 0.043 s
% 5.62/1.13 % (1523173)Peak memory usage: 14 MB
% 5.62/1.13 % (1523173)Instructions burned: 162 (million)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523183)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4248720744:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 5.62/1.13 % (1523171)Instruction limit reached!
% 5.62/1.13 % (1523171)------------------------------
% 5.62/1.13 % (1523171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523171)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523171)Termination reason: Instruction limit
% 5.62/1.13 % (1523171)Termination phase: Saturation
% 5.62/1.13 % (1523171)Time elapsed: 0.069 s
% 5.62/1.13 % (1523171)Peak memory usage: 13 MB
% 5.62/1.13 % (1523171)Instructions burned: 118 (million)
% 5.62/1.13 % (1523184)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1594776825:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.62/1.13 % (1523172)Instruction limit reached!
% 5.62/1.13 % (1523172)------------------------------
% 5.62/1.13 % (1523172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523172)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523172)Termination reason: Instruction limit
% 5.62/1.13 % (1523172)Termination phase: Saturation
% 5.62/1.13 % (1523172)Time elapsed: 0.060 s
% 5.62/1.13 % (1523172)Peak memory usage: 14 MB
% 5.62/1.13 % (1523172)Instructions burned: 132 (million)
% 5.62/1.13 % (1523184)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.62/1.13 % (1523184)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.62/1.13 % (1523187)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1956472618:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.62/1.13 % (1523189)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=20785596:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 5.62/1.13 % (1523186)ott-21_1_sil=16000:fs=off:random_seed=2103925383:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.62/1.13 % (1523183)Instruction limit reached!
% 5.62/1.13 % (1523183)------------------------------
% 5.62/1.13 % (1523183)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523183)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523183)Termination reason: Instruction limit
% 5.62/1.13 % (1523183)Termination phase: Saturation
% 5.62/1.13 % (1523183)Time elapsed: 0.061 s
% 5.62/1.13 % (1523183)Peak memory usage: 13 MB
% 5.62/1.13 % (1523183)Instructions burned: 131 (million)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523193)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1739589499:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.62/1.13 % (1523194)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=746658423:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523197)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=642370369:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 5.62/1.13 % (1523197)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.62/1.13 % (1523186)Instruction limit reached!
% 5.62/1.13 % (1523186)------------------------------
% 5.62/1.13 % (1523186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523186)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523186)Termination reason: Instruction limit
% 5.62/1.13 % (1523186)Termination phase: Saturation
% 5.62/1.13 % (1523186)Time elapsed: 0.148 s
% 5.62/1.13 % (1523186)Peak memory usage: 13 MB
% 5.62/1.13 % (1523186)Instructions burned: 182 (million)
% 5.62/1.13 % (1523184)Instruction limit reached!
% 5.62/1.13 % (1523184)------------------------------
% 5.62/1.13 % (1523184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523184)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523184)Termination reason: Instruction limit
% 5.62/1.13 % (1523184)Termination phase: Saturation
% 5.62/1.13 % (1523184)Time elapsed: 0.193 s
% 5.62/1.13 % (1523184)Peak memory usage: 18 MB
% 5.62/1.13 % (1523184)Instructions burned: 686 (million)
% 5.62/1.13 % (1523199)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3793058012:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 5.62/1.13 % (1523200)fmb+10_1_sil=64000:random_seed=3630239189:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.62/1.13 % (1523200)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523199)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.62/1.13 % (1523203)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=4081993411:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523207)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2934101423:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523209)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2542249803:i=5131_2995 on theBenchmark for (2995ds/5131Mi)
% 5.62/1.13 % (1523209)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.62/1.13 % (1523187)Instruction limit reached!
% 5.62/1.13 % (1523187)------------------------------
% 5.62/1.13 % (1523187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523187)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523187)Termination reason: Instruction limit
% 5.62/1.13 % (1523187)Termination phase: Saturation
% 5.62/1.13 % (1523187)Time elapsed: 0.303 s
% 5.62/1.13 % (1523187)Peak memory usage: 14 MB
% 5.62/1.13 % (1523187)Instructions burned: 478 (million)
% 5.62/1.13 % (1523211)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=84910605:i=1472:ins=7:fdi=8:gsp=on_2995 on theBenchmark for (2995ds/1472Mi)
% 5.62/1.13 % (1523211)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.62/1.13 % (1523211)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.62/1.13 % (1523197)Instruction limit reached!
% 5.62/1.13 % (1523197)------------------------------
% 5.62/1.13 % (1523197)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523197)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523197)Termination reason: Instruction limit
% 5.62/1.13 % (1523197)Termination phase: Saturation
% 5.62/1.13 % (1523197)Time elapsed: 0.354 s
% 5.62/1.13 % (1523197)Peak memory usage: 19 MB
% 5.62/1.13 % (1523197)Instructions burned: 693 (million)
% 5.62/1.13 % (1523213)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2224183198:i=6324_2993 on theBenchmark for (2993ds/6324Mi)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523215)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=659654042:fmbsr=2.30978:i=2174_2993 on theBenchmark for (2993ds/2174Mi)
% 5.62/1.13 % Exception at run slice level
% 5.62/1.13 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.62/1.13 % (1523217)ott-2_1_sil=16000:newcnf=on:random_seed=1778347433:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2992 on theBenchmark for (2992ds/869Mi)
% 5.62/1.13 % (1523217)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.62/1.13 % (1523193)Instruction limit reached!
% 5.62/1.13 % (1523193)------------------------------
% 5.62/1.13 % (1523193)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523193)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523193)Termination reason: Instruction limit
% 5.62/1.13 % (1523193)Termination phase: Saturation
% 5.62/1.13 % (1523193)Time elapsed: 0.594 s
% 5.62/1.13 % (1523193)Peak memory usage: 21 MB
% 5.62/1.13 % (1523193)Instructions burned: 1180 (million)
% 5.62/1.13 % (1523220)ott+10_1_sil=32000:tgt=ground:random_seed=1669613319:i=5114:av=off_2992 on theBenchmark for (2992ds/5114Mi)
% 5.62/1.13 % (1523217) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1523161-1523217"...
% 5.62/1.13 % (1523217)...printing done.
% 5.62/1.13 % (1523217)Refutation found. Thanks to Tanya!
% 5.62/1.13 % SZS status Theorem for theBenchmark
% 5.62/1.13 % SZS output start Proof for theBenchmark
% 5.62/1.13 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 5.62/1.13 thf(type_def_6, type, real: $tType).
% 5.62/1.13 thf(type_def_7, type, set: $tType > $tType).
% 5.62/1.13 thf(type_def_8, type, a: $tType).
% 5.62/1.13 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 5.62/1.13 thf(func_def_0, type, ordere890947078_space: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_3, type, plus: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_4, type, zero: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_5, type, ord: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_6, type, neg_numeral: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_7, type, order: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_8, type, group_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_9, type, monoid_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_11, type, preorder: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_12, type, zero_neq_one: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_13, type, zero_less_one: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_14, type, semigroup_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_15, type, linordered_idom: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_16, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_17, type, linordered_field: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_18, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_19, type, linordered_semidom: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_20, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_21, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_22, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_23, type, ordere216010020id_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_24, type, real_V1076094709vector: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_25, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_26, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_27, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_28, type, ordere1818651114id_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_29, type, strict797366125id_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_30, type, real_V55928688vector: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_31, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_32, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_33, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_34, type, real_V1587248058vector: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_35, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_36, type, ordere516151231imp_le: !>[X0: $tType]:($o)).
% 5.62/1.13 thf(func_def_37, type, unique455577585es_aux: !>[X0: $tType]:((product_prod @ X0 @ X0 > $o))).
% 5.62/1.13 thf(func_def_38, type, one_one: !>[X0: $tType]:(X0)).
% 5.62/1.13 thf(func_def_39, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 5.62/1.13 thf(func_def_40, type, zero_zero: !>[X0: $tType]:(X0)).
% 5.62/1.13 thf(func_def_41, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.62/1.13 thf(func_def_42, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.62/1.13 thf(func_def_43, type, prefer1289595409x_pref: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > $o))).
% 5.62/1.13 thf(func_def_44, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 5.62/1.13 thf(func_def_45, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 5.62/1.13 thf(func_def_46, type, real_V1908273582scaleR: !>[X0: $tType]:((real > X0 > X0))).
% 5.62/1.13 thf(func_def_47, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 5.62/1.13 thf(func_def_48, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 5.62/1.13 thf(func_def_49, type, relation: set @ product_prod @ a @ a).
% 5.62/1.13 thf(func_def_50, type, u: real).
% 5.62/1.13 thf(func_def_51, type, v: real).
% 5.62/1.13 thf(func_def_52, type, x: a).
% 5.62/1.13 thf(func_def_53, type, y: a).
% 5.62/1.13 thf(func_def_57, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.62/1.13 thf(func_def_58, type, vAND: ($o > $o > $o)).
% 5.62/1.13 thf(func_def_59, type, db0: !>[X0: $tType]:(X0)).
% 5.62/1.13 thf(func_def_60, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.62/1.13 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.62/1.13 thf(func_def_62, type, db2: !>[X0: $tType]:(X0)).
% 5.62/1.13 thf(func_def_63, type, db1: !>[X0: $tType]:(X0)).
% 5.62/1.13 thf(func_def_64, type, vOR: ($o > $o > $o)).
% 5.62/1.13 thf(func_def_65, type, vNOT: ($o > $o)).
% 5.62/1.13 thf(func_def_66, type, vIMP: ($o > $o > $o)).
% 5.62/1.13 thf(func_def_67, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.62/1.13 thf(func_def_68, type, db3: !>[X0: $tType]:(X0)).
% 5.62/1.13 thf(func_def_69, type, db4: !>[X0: $tType]:(X0)).
% 5.62/1.13 thf(func_def_70, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 5.62/1.13 thf(func_def_71, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 5.62/1.13 thf(func_def_72, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 5.62/1.13 thf(func_def_73, type, sK3: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_74, type, sK4: !>[X0: $tType]:((X0 > X0 > X0))).
% 5.62/1.13 thf(func_def_75, type, sK5: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 5.62/1.13 thf(func_def_76, type, sK6: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 5.62/1.13 thf(func_def_77, type, sK7: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > real))).
% 5.62/1.13 thf(func_def_78, type, sK8: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > real))).
% 5.62/1.13 thf(func_def_79, type, sK9: !>[X0: $tType]:((set @ X0 > set @ X0 > X0 > X0))).
% 5.62/1.13 thf(func_def_80, type, sK10: !>[X0: $tType]:((set @ X0 > set @ X0 > X0 > X0))).
% 5.62/1.13 thf(func_def_81, type, sK11: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 5.62/1.13 thf(func_def_82, type, sK12: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_83, type, sK13: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 5.62/1.13 thf(func_def_84, type, sK14: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 5.62/1.13 thf(func_def_85, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6))).
% 5.62/1.13 thf(func_def_86, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 5.62/1.13 thf(func_def_87, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 5.62/1.13 thf(func_def_88, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 5.62/1.13 thf(func_def_89, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 5.62/1.13 thf(func_def_90, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 5.62/1.13 thf(func_def_91, type, sK21: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_92, type, sK22: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5))).
% 5.62/1.13 thf(func_def_93, type, sK23: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 5.62/1.13 thf(func_def_94, type, sK24: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 5.62/1.13 thf(func_def_95, type, sK25: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 5.62/1.13 thf(func_def_96, type, sK26: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 5.62/1.13 thf(func_def_97, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_98, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4))).
% 5.62/1.13 thf(func_def_99, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 5.62/1.13 thf(func_def_100, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 5.62/1.13 thf(func_def_101, type, sK31: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 5.62/1.13 thf(func_def_102, type, sK32: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_103, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 5.62/1.13 thf(func_def_104, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 5.62/1.13 thf(func_def_105, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 5.62/1.13 thf(func_def_106, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_107, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 5.62/1.13 thf(func_def_108, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 5.62/1.13 thf(func_def_109, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_110, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0))).
% 5.62/1.13 thf(func_def_111, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1))).
% 5.62/1.13 thf(func_def_112, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2))).
% 5.62/1.13 thf(func_def_113, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3))).
% 5.62/1.13 thf(func_def_114, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4))).
% 5.62/1.13 thf(func_def_115, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5))).
% 5.62/1.13 thf(func_def_116, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6))).
% 5.62/1.13 thf(func_def_117, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0))).
% 5.62/1.13 thf(func_def_118, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1))).
% 5.62/1.13 thf(func_def_119, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2))).
% 5.62/1.13 thf(func_def_120, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3))).
% 5.62/1.13 thf(func_def_121, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4))).
% 5.62/1.13 thf(func_def_122, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5))).
% 5.62/1.13 thf(func_def_123, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 5.62/1.13 thf(func_def_124, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 5.62/1.13 thf(func_def_125, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 5.62/1.13 thf(func_def_126, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 5.62/1.13 thf(func_def_127, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 5.62/1.13 thf(func_def_128, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 5.62/1.13 thf(func_def_129, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 5.62/1.13 thf(func_def_130, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 5.62/1.13 thf(func_def_131, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 5.62/1.13 thf(func_def_132, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 5.62/1.13 thf(func_def_133, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 5.62/1.13 thf(func_def_134, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 5.62/1.13 thf(func_def_135, type, sK65: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 5.62/1.13 thf(func_def_136, type, sK66: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_137, type, sK67: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 5.62/1.13 thf(func_def_138, type, sK68: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 5.62/1.13 thf(func_def_139, type, sK69: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 5.62/1.13 thf(func_def_140, type, sK70: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > X0))).
% 5.62/1.13 thf(func_def_141, type, sK71: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > real))).
% 5.62/1.13 thf(func_def_142, type, sK72: !>[X0: $tType]:((set @ product_prod @ X0 @ X0 > real))).
% 5.62/1.13 thf(func_def_143, type, sK73: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 5.62/1.13 thf(func_def_144, type, sK74: !>[X0: $tType]:((X0 > X0 > X0))).
% 5.62/1.13 thf(func_def_145, type, sK75: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 5.62/1.13 thf(func_def_146, type, sK76: !>[X0: $tType]:((X0 > X0 > X0))).
% 5.62/1.13 thf(func_def_147, type, sK77: !>[X0: $tType]:((X0 > X0))).
% 5.62/1.13 thf(func_def_148, type, sK78: !>[X0: $tType]:((X0 > X0))).
% 5.62/1.13 thf(func_def_149, type, sK79: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 5.62/1.13 thf(func_def_150, type, sK80: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 5.62/1.13 thf(func_def_151, type, sK81: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 5.62/1.13 thf(func_def_152, type, sK82: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 5.62/1.13 thf(func_def_153, type, sK83: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 5.62/1.13 thf(func_def_154, type, sK84: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 5.62/1.13 thf(func_def_155, type, sK85: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 5.62/1.13 thf(func_def_156, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 5.62/1.13 thf(func_def_157, type, sK87: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 5.62/1.13 thf(func_def_158, type, sK88: !>[X0: $tType]:(((X0 > $o) > (X0 > real) > (X0 > $o) > real))).
% 5.62/1.13 thf(func_def_159, type, sK89: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > real > (X0 > real) > X0))).
% 5.62/1.13 thf(func_def_160, type, sK90: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > real) > real))).
% 5.62/1.13 thf(func_def_161, type, sK91: !>[X0: $tType]:(((X0 > $o) > (X0 > real) > (X0 > $o) > real > X0))).
% 5.62/1.13 thf(func_def_162, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > real) > (X0 > $o) > real > X0))).
% 5.62/1.13 thf(func_def_163, type, sK93: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 5.62/1.13 thf(f6,axiom,(
% 5.62/1.13 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_assms_I2_J)).
% 5.62/1.13 thf(f7,axiom,(
% 5.62/1.13 ((u != one_one @ real) & (u != zero_zero @ real)) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6__092_060open_062u_A_092_060noteq_062_A0_A_092_060and_062_Au_A_092_060noteq_062_A1_A_092_060longrightarrow_062_Au_A_K_092_060_094sub_062R_Ax_A_L_Av_A_K_092_060_094sub_062R_Ay_A_092_060succeq_062_Ay_092_060close_062)).
% 5.62/1.13 thf(f8,axiom,(
% 5.62/1.13 (u = zero_zero @ real) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_u__0)).
% 5.62/1.13 thf(f10,axiom,(
% 5.62/1.13 (((plus_plus @ real @ u @ v)) = one_one @ real)),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_assms_I5_J)).
% 5.62/1.13 thf(f32,axiom,(
% 5.62/1.13 ! [X0 : $tType] : (monoid_add @ X0 => ! [X1 : X0] : (((plus_plus @ X0 @ X1 @ zero_zero @ X0)) = X1))),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add_Oright__neutral)).
% 5.62/1.13 thf(f75,axiom,(
% 5.62/1.13 ! [X0 : $tType] : (cancel_semigroup_add @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((((plus_plus @ X0 @ X1 @ X2)) = ((plus_plus @ X0 @ X1 @ X3))) => (X2 = X3)))),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_add__left__imp__eq)).
% 5.62/1.13 thf(f115,axiom,(
% 5.62/1.13 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X1 : X0] : (((real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1)) = zero_zero @ X0))),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_scale__zero__left)).
% 5.62/1.13 thf(f117,axiom,(
% 5.62/1.13 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X1 : X0] : (((real_V1908273582scaleR @ X0 @ one_one @ real @ X1)) = X1))),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_scaleR__one)).
% 5.62/1.13 thf(f259,axiom,(
% 5.62/1.13 ! [X0 : $tType] : (real_V1076094709vector @ X0 => monoid_add @ X0)),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Oreal__vector___Groups_Omonoid__add)).
% 5.62/1.13 thf(f298,axiom,(
% 5.62/1.13 cancel_semigroup_add @ real),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__semigroup__add)).
% 5.62/1.13 thf(f309,axiom,(
% 5.62/1.13 monoid_add @ real),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__add_13)).
% 5.62/1.13 thf(f340,axiom,(
% 5.62/1.13 real_V1076094709vector @ a),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0)).
% 5.62/1.13 thf(f341,conjecture,(
% 5.62/1.13 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 5.62/1.13 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 5.62/1.13 thf(f342,negated_conjecture,(
% 5.62/1.13 ~(member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 5.62/1.13 inference(negated_conjecture,[status(cth)],[f341])).
% 5.62/1.13 thf(f353,plain,(
% 5.62/1.13 (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)),
% 5.62/1.13 inference(rectify,[],[f6])).
% 5.62/1.13 thf(f354,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $true)),
% 5.62/1.13 inference(fool_elimination,[],[f353])).
% 5.62/1.13 thf(f355,plain,(
% 5.62/1.13 ((u != one_one @ real) & (u != zero_zero @ real)) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 5.62/1.13 inference(rectify,[],[f7])).
% 5.62/1.13 thf(f356,plain,(
% 5.62/1.13 ((u != one_one @ real) & (u != zero_zero @ real)) => (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true)),
% 5.62/1.13 inference(fool_elimination,[],[f355])).
% 5.62/1.13 thf(f357,plain,(
% 5.62/1.13 (u = zero_zero @ real) => (member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 5.62/1.13 inference(rectify,[],[f8])).
% 5.62/1.13 thf(f358,plain,(
% 5.62/1.13 (u = zero_zero @ real) => (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true)),
% 5.62/1.13 inference(fool_elimination,[],[f357])).
% 5.62/1.13 thf(f401,plain,(
% 5.62/1.13 ! [X0 : $tType] : (monoid_add @ X0 => ! [X1 : X0] : (((plus_plus @ X0 @ X1 @ zero_zero @ X0)) = X1))),
% 5.62/1.13 inference(rectify,[],[f32])).
% 5.62/1.13 thf(f402,plain,(
% 5.62/1.13 ! [X0 : $tType] : ((monoid_add @ X0 = $true) => ! [X1 : X0] : (((plus_plus @ X0 @ X1 @ zero_zero @ X0)) = X1))),
% 5.62/1.13 inference(fool_elimination,[],[f401])).
% 5.62/1.13 thf(f483,plain,(
% 5.62/1.13 ! [X0 : $tType] : (cancel_semigroup_add @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((((plus_plus @ X0 @ X1 @ X2)) = ((plus_plus @ X0 @ X1 @ X3))) => (X2 = X3)))),
% 5.62/1.13 inference(rectify,[],[f75])).
% 5.62/1.13 thf(f484,plain,(
% 5.62/1.13 ! [X0 : $tType] : ((cancel_semigroup_add @ X0 = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((((plus_plus @ X0 @ X1 @ X3)) = ((plus_plus @ X0 @ X1 @ X2))) => (X2 = X3)))),
% 5.62/1.13 inference(fool_elimination,[],[f483])).
% 5.62/1.13 thf(f547,plain,(
% 5.62/1.13 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X1 : X0] : (((real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1)) = zero_zero @ X0))),
% 5.62/1.13 inference(rectify,[],[f115])).
% 5.62/1.13 thf(f548,plain,(
% 5.62/1.13 ! [X0 : $tType] : ((real_V1076094709vector @ X0 = $true) => ! [X1 : X0] : (zero_zero @ X0 = ((real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1))))),
% 5.62/1.13 inference(fool_elimination,[],[f547])).
% 5.62/1.13 thf(f551,plain,(
% 5.62/1.13 ! [X0 : $tType] : (real_V1076094709vector @ X0 => ! [X1 : X0] : (((real_V1908273582scaleR @ X0 @ one_one @ real @ X1)) = X1))),
% 5.62/1.13 inference(rectify,[],[f117])).
% 5.62/1.13 thf(f552,plain,(
% 5.62/1.13 ! [X0 : $tType] : ((real_V1076094709vector @ X0 = $true) => ! [X1 : X0] : (((real_V1908273582scaleR @ X0 @ one_one @ real @ X1)) = X1))),
% 5.62/1.13 inference(fool_elimination,[],[f551])).
% 5.62/1.13 thf(f833,plain,(
% 5.62/1.13 ! [X0 : $tType] : (real_V1076094709vector @ X0 => monoid_add @ X0)),
% 5.62/1.13 inference(rectify,[],[f259])).
% 5.62/1.13 thf(f834,plain,(
% 5.62/1.13 ! [X0 : $tType] : ((real_V1076094709vector @ X0 = $true) => (monoid_add @ X0 = $true))),
% 5.62/1.13 inference(fool_elimination,[],[f833])).
% 5.62/1.13 thf(f911,plain,(
% 5.62/1.13 cancel_semigroup_add @ real),
% 5.62/1.13 inference(rectify,[],[f298])).
% 5.62/1.13 thf(f912,plain,(
% 5.62/1.13 (cancel_semigroup_add @ real = $true)),
% 5.62/1.13 inference(fool_elimination,[],[f911])).
% 5.62/1.13 thf(f933,plain,(
% 5.62/1.13 monoid_add @ real),
% 5.62/1.13 inference(rectify,[],[f309])).
% 5.62/1.13 thf(f934,plain,(
% 5.62/1.13 (monoid_add @ real = $true)),
% 5.62/1.13 inference(fool_elimination,[],[f933])).
% 5.62/1.13 thf(f995,plain,(
% 5.62/1.13 real_V1076094709vector @ a),
% 5.62/1.13 inference(rectify,[],[f340])).
% 5.62/1.13 thf(f996,plain,(
% 5.62/1.13 (real_V1076094709vector @ a = $true)),
% 5.62/1.13 inference(fool_elimination,[],[f995])).
% 5.62/1.13 thf(f997,plain,(
% 5.62/1.13 ~(member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)),
% 5.62/1.13 inference(rectify,[],[f342])).
% 5.62/1.13 thf(f998,plain,(
% 5.62/1.13 ~ (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true)),
% 5.62/1.13 inference(fool_elimination,[],[f997])).
% 5.62/1.13 thf(f1010,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) != $true)),
% 5.62/1.13 inference(flattening,[],[f998])).
% 5.62/1.13 thf(f1019,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true) | ((u = one_one @ real) | (u = zero_zero @ real))),
% 5.62/1.13 inference(ennf_transformation,[],[f356])).
% 5.62/1.13 thf(f1020,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true) | (u = one_one @ real) | (u = zero_zero @ real)),
% 5.62/1.13 inference(flattening,[],[f1019])).
% 5.62/1.13 thf(f1021,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true) | (u != zero_zero @ real)),
% 5.62/1.13 inference(ennf_transformation,[],[f358])).
% 5.62/1.13 thf(f1044,plain,(
% 5.62/1.13 ! [X0 : $tType] : (! [X1 : X0] : (((plus_plus @ X0 @ X1 @ zero_zero @ X0)) = X1) | (monoid_add @ X0 != $true))),
% 5.62/1.13 inference(ennf_transformation,[],[f402])).
% 5.62/1.13 thf(f1099,plain,(
% 5.62/1.13 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((X2 = X3) | (((plus_plus @ X0 @ X1 @ X3)) != ((plus_plus @ X0 @ X1 @ X2)))) | (cancel_semigroup_add @ X0 != $true))),
% 5.62/1.13 inference(ennf_transformation,[],[f484])).
% 5.62/1.13 thf(f1140,plain,(
% 5.62/1.13 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero @ X0 = ((real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1))) | (real_V1076094709vector @ X0 != $true))),
% 5.62/1.13 inference(ennf_transformation,[],[f548])).
% 5.62/1.13 thf(f1142,plain,(
% 5.62/1.13 ! [X0 : $tType] : (! [X1 : X0] : (((real_V1908273582scaleR @ X0 @ one_one @ real @ X1)) = X1) | (real_V1076094709vector @ X0 != $true))),
% 5.62/1.13 inference(ennf_transformation,[],[f552])).
% 5.62/1.13 thf(f1330,plain,(
% 5.62/1.13 ! [X0 : $tType] : ((monoid_add @ X0 = $true) | (real_V1076094709vector @ X0 != $true))),
% 5.62/1.13 inference(ennf_transformation,[],[f834])).
% 5.62/1.13 thf(f1441,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $true)),
% 5.62/1.13 inference(cnf_transformation,[],[f354])).
% 5.62/1.13 thf(f1442,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true) | (u = one_one @ real) | (u = zero_zero @ real)),
% 5.62/1.13 inference(cnf_transformation,[],[f1020])).
% 5.62/1.13 thf(f1443,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $true) | (u != zero_zero @ real)),
% 5.62/1.13 inference(cnf_transformation,[],[f1021])).
% 5.62/1.13 thf(f1445,plain,(
% 5.62/1.13 (one_one @ real = ((plus_plus @ real @ u @ v)))),
% 5.62/1.13 inference(cnf_transformation,[],[f10])).
% 5.62/1.13 thf(f1467,plain,(
% 5.62/1.13 ( ! [X0 : $tType,X1 : X0] : ((((plus_plus @ X0 @ X1 @ zero_zero @ X0)) = X1) | (monoid_add @ X0 != $true)) )),
% 5.62/1.13 inference(cnf_transformation,[],[f1044])).
% 5.62/1.13 thf(f1514,plain,(
% 5.62/1.13 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((((plus_plus @ X0 @ X1 @ X3)) != ((plus_plus @ X0 @ X1 @ X2))) | (X2 = X3) | (cancel_semigroup_add @ X0 != $true)) )),
% 5.62/1.13 inference(cnf_transformation,[],[f1099])).
% 5.62/1.13 thf(f1557,plain,(
% 5.62/1.13 ( ! [X0 : $tType,X1 : X0] : ((zero_zero @ X0 = ((real_V1908273582scaleR @ X0 @ zero_zero @ real @ X1))) | (real_V1076094709vector @ X0 != $true)) )),
% 5.62/1.13 inference(cnf_transformation,[],[f1140])).
% 5.62/1.13 thf(f1559,plain,(
% 5.62/1.13 ( ! [X0 : $tType,X1 : X0] : ((((real_V1908273582scaleR @ X0 @ one_one @ real @ X1)) = X1) | (real_V1076094709vector @ X0 != $true)) )),
% 5.62/1.13 inference(cnf_transformation,[],[f1142])).
% 5.62/1.13 thf(f1730,plain,(
% 5.62/1.13 ( ! [X0 : $tType] : ((monoid_add @ X0 = $true) | (real_V1076094709vector @ X0 != $true)) )),
% 5.62/1.13 inference(cnf_transformation,[],[f1330])).
% 5.62/1.13 thf(f1769,plain,(
% 5.62/1.13 (cancel_semigroup_add @ real = $true)),
% 5.62/1.13 inference(cnf_transformation,[],[f912])).
% 5.62/1.13 thf(f1780,plain,(
% 5.62/1.13 (monoid_add @ real = $true)),
% 5.62/1.13 inference(cnf_transformation,[],[f934])).
% 5.62/1.13 thf(f1811,plain,(
% 5.62/1.13 (real_V1076094709vector @ a = $true)),
% 5.62/1.13 inference(cnf_transformation,[],[f996])).
% 5.62/1.13 thf(f1812,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) != $true)),
% 5.62/1.13 inference(cnf_transformation,[],[f1010])).
% 5.62/1.13 thf(f1814,definition,(
% 5.62/1.13 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 5.62/1.13 introduced(theory,[fool_exhaustiveness_axiom])).
% 5.62/1.13 thf(f2197,plain,(
% 5.62/1.13 (u != zero_zero @ real)),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f1443,f1812])).
% 5.62/1.13 thf(f2198,plain,(
% 5.62/1.13 (u = one_one @ real) | (u = zero_zero @ real)),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f1442,f1812])).
% 5.62/1.13 thf(f2199,plain,(
% 5.62/1.13 (u = one_one @ real)),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f2198,f2197])).
% 5.62/1.13 thf(f2209,plain,(
% 5.62/1.13 ($true != $true) | (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $false)),
% 5.62/1.13 inference(constrained_superposition,[],[f1812,f1814])).
% 5.62/1.13 thf(f2210,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ u @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)) = $false)),
% 5.62/1.13 inference(trivial_inequality_removal,[],[f2209])).
% 5.62/1.13 thf(f2211,plain,(
% 5.62/1.13 ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ (real_V1908273582scaleR @ a @ one_one @ real @ x) @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)))),
% 5.62/1.13 inference(forward_demodulation,[],[f2210,f2199])).
% 5.62/1.13 thf(f2236,plain,(
% 5.62/1.13 (one_one @ real = ((plus_plus @ real @ one_one @ real @ v)))),
% 5.62/1.13 inference(constrained_superposition,[],[f1445,f2199])).
% 5.62/1.13 thf(f2394,definition,(
% 5.62/1.13 spl94_19 <=> ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)))),
% 5.62/1.13 introduced(definition,[new_symbols(definition,[spl94_19])],[avatar_definition])).
% 5.62/1.13 thf(f2396,plain,(
% 5.62/1.13 ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation))) | ~spl94_19),
% 5.62/1.13 inference(avatar_component_clause,[],[f2394])).
% 5.62/1.13 thf(f2405,plain,(
% 5.62/1.13 ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation))) | (real_V1076094709vector @ a != $true)),
% 5.62/1.13 inference(constrained_superposition,[],[f2211,f1559])).
% 5.62/1.13 thf(f2408,plain,(
% 5.62/1.13 ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ (real_V1908273582scaleR @ a @ v @ y)) @ y) @ relation)))),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f2405,f1811])).
% 5.62/1.13 thf(f2410,plain,(
% 5.62/1.13 spl94_19),
% 5.62/1.13 inference(avatar_split_clause,[],[f2408,f2394])).
% 5.62/1.13 thf(f2691,plain,(
% 5.62/1.13 ( ! [X0 : real] : ((one_one @ real != ((plus_plus @ real @ one_one @ real @ X0))) | (v = X0) | (cancel_semigroup_add @ real != $true)) )),
% 5.62/1.13 inference(constrained_superposition,[],[f1514,f2236])).
% 5.62/1.13 thf(f2697,plain,(
% 5.62/1.13 ( ! [X0 : real] : ((one_one @ real != ((plus_plus @ real @ one_one @ real @ X0))) | (v = X0)) )),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f2691,f1769])).
% 5.62/1.13 thf(f2705,plain,(
% 5.62/1.13 (one_one @ real != one_one @ real) | (zero_zero @ real = v) | (monoid_add @ real != $true)),
% 5.62/1.13 inference(constrained_superposition,[],[f2697,f1467])).
% 5.62/1.13 thf(f2706,plain,(
% 5.62/1.13 (zero_zero @ real = v) | (monoid_add @ real != $true)),
% 5.62/1.13 inference(trivial_inequality_removal,[],[f2705])).
% 5.62/1.13 thf(f2709,plain,(
% 5.62/1.13 (zero_zero @ real = v)),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f2706,f1780])).
% 5.62/1.13 thf(f2722,plain,(
% 5.62/1.13 ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ (real_V1908273582scaleR @ a @ zero_zero @ real @ y)) @ y) @ relation))) | ~spl94_19),
% 5.62/1.13 inference(constrained_superposition,[],[f2396,f2709])).
% 5.62/1.13 thf(f2730,plain,(
% 5.62/1.13 ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ zero_zero @ a) @ y) @ relation))) | (real_V1076094709vector @ a != $true) | ~spl94_19),
% 5.62/1.13 inference(constrained_superposition,[],[f2722,f1557])).
% 5.62/1.13 thf(f2734,plain,(
% 5.62/1.13 ($false = ((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ (plus_plus @ a @ x @ zero_zero @ a) @ y) @ relation))) | ~spl94_19),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f2730,f1811])).
% 5.62/1.13 thf(f2737,plain,(
% 5.62/1.13 (((member @ product_prod @ a @ a @ (product_Pair @ a @ a @ x @ y) @ relation)) = $false) | ($true != monoid_add @ a) | ~spl94_19),
% 5.62/1.13 inference(constrained_superposition,[],[f2734,f1467])).
% 5.62/1.13 thf(f2740,plain,(
% 5.62/1.13 ($true = $false) | ($true != monoid_add @ a) | ~spl94_19),
% 5.62/1.13 inference(forward_demodulation,[],[f2737,f1441])).
% 5.62/1.13 thf(f2741,plain,(
% 5.62/1.13 ($true != monoid_add @ a) | ~spl94_19),
% 5.62/1.13 inference(trivial_inequality_removal,[],[f2740])).
% 5.62/1.13 thf(f2745,plain,(
% 5.62/1.13 ($true != $true) | (real_V1076094709vector @ a != $true) | ~spl94_19),
% 5.62/1.13 inference(constrained_superposition,[],[f2741,f1730])).
% 5.62/1.13 thf(f2746,plain,(
% 5.62/1.13 (real_V1076094709vector @ a != $true) | ~spl94_19),
% 5.62/1.13 inference(trivial_inequality_removal,[],[f2745])).
% 5.62/1.13 thf(f2748,plain,(
% 5.62/1.13 $false | ~spl94_19),
% 5.62/1.13 inference(forward_subsumption_resolution,[],[f2746,f1811])).
% 5.62/1.13 thf(f2749,plain,(
% 5.62/1.13 ~spl94_19),
% 5.62/1.13 inference(avatar_contradiction_clause,[],[f2748])).
% 5.62/1.13 cnf(s18, plain, spl94_19, inference(sat_conversion,[],[f2410])).
% 5.62/1.13 cnf(s35, plain, ~spl94_19, inference(sat_conversion,[],[f2749])).
% 5.62/1.13 cnf(s36, plain, $false, inference(rat,[],[s18,s35])).
% 5.62/1.13 thf(f2750,plain,(
% 5.62/1.13 $false),
% 5.62/1.13 inference(avatar_sat_refutation,[],[s36])).
% 5.62/1.13 % SZS output end Proof for theBenchmark
% 5.62/1.13 % (1523217)------------------------------
% 5.62/1.13 % (1523217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.62/1.13 % (1523217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.62/1.13 % (1523217)CaDiCaL version: 2.1.3
% 5.62/1.13 % (1523217)Termination reason: Refutation
% 5.62/1.13 % (1523217)Time elapsed: 0.148 s
% 5.62/1.13 % (1523217)Peak memory usage: 14 MB
% 5.62/1.13 % (1523217)Instructions burned: 205 (million)
% 5.62/1.13 % (1523161)Success in time 0.899 s
% 5.62/1.13 % Vampire exiting
%------------------------------------------------------------------------------