%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP198^2 : 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 : n008.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 08:11:05 AM UTC 2026
% Result : Theorem 2.46s 0.63s
% Output : Refutation 2.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP198^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n008.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 20:11:24 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 2.46/0.63 % (3669850)Will run a generic schedule for satisfiability detection.
% 2.46/0.63 % (3669860)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1575675573:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.46/0.63 % (3669856)% WARNING: option uhcvi not known.
% 2.46/0.63 % (3669856)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=247132147:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.46/0.63 % (3669857)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3156037766:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.46/0.63 % (3669855)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3629321663_2999 on theBenchmark for (2999ds/0Mi)
% 2.46/0.63 % (3669858)dis+10_1_sil=32000:sp=arity:random_seed=4263111405:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.46/0.63 % (3669859)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2075993969:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.46/0.63 % (3669861)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3144051468:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.46/0.63 % (3669856)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.46/0.63 % (3669859)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.46/0.63 % (3669860)Instruction limit reached!
% 2.46/0.63 % (3669860)------------------------------
% 2.46/0.63 % (3669860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.63 % (3669860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.63 % (3669860)CaDiCaL version: 2.1.3
% 2.46/0.63 % (3669860)Termination reason: Instruction limit
% 2.46/0.63 % (3669860)Termination phase: Saturation
% 2.46/0.63 % (3669860)Time elapsed: 0.032 s
% 2.46/0.63 % (3669860)Peak memory usage: 13 MB
% 2.46/0.63 % (3669860)Instructions burned: 132 (million)
% 2.46/0.63 % (3669869)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1931372891:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.46/0.63 % (3669858)Instruction limit reached!
% 2.46/0.63 % (3669858)------------------------------
% 2.46/0.63 % (3669858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.63 % (3669858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.63 % (3669858)CaDiCaL version: 2.1.3
% 2.46/0.63 % (3669858)Termination reason: Instruction limit
% 2.46/0.63 % (3669858)Termination phase: Property scanning
% 2.46/0.63 % (3669858)Time elapsed: 0.047 s
% 2.46/0.63 % (3669858)Peak memory usage: 12 MB
% 2.46/0.63 % (3669858)Instructions burned: 104 (million)
% 2.46/0.63 % Exception at run slice level
% 2.46/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.46/0.63 % (3669856)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.46/0.63 % (3669859)Instruction limit reached!
% 2.46/0.63 % (3669859)------------------------------
% 2.46/0.63 % (3669859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.63 % (3669859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.63 % (3669859)CaDiCaL version: 2.1.3
% 2.46/0.63 % (3669859)Termination reason: Instruction limit
% 2.46/0.63 % (3669859)Termination phase: Saturation
% 2.46/0.63 % (3669859)Time elapsed: 0.053 s
% 2.46/0.63 % (3669859)Peak memory usage: 12 MB
% 2.46/0.63 % (3669859)Instructions burned: 116 (million)
% 2.46/0.63 % Exception at run slice level
% 2.46/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.46/0.63 % (3669871)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=979409910:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.46/0.63 % (3669873)ott-21_1_sil=16000:fs=off:random_seed=1498523482:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.46/0.63 % (3669872)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=882896427:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.46/0.63 % (3669874)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=237260642:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.46/0.63 % (3669872)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.46/0.63 % (3669871)Instruction limit reached!
% 2.46/0.63 % (3669871)------------------------------
% 2.46/0.63 % (3669871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.63 % (3669871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.63 % (3669871)CaDiCaL version: 2.1.3
% 2.46/0.63 % (3669871)Termination reason: Instruction limit
% 2.46/0.63 % (3669871)Termination phase: Saturation
% 2.46/0.63 % (3669871)Time elapsed: 0.060 s
% 2.46/0.63 % (3669871)Peak memory usage: 13 MB
% 2.46/0.63 % (3669872)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.46/0.63 % (3669871)Instructions burned: 132 (million)
% 2.46/0.63 % (3669861)Instruction limit reached!
% 2.46/0.63 % (3669861)------------------------------
% 2.46/0.63 % (3669861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.63 % (3669861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.63 % (3669861)CaDiCaL version: 2.1.3
% 2.46/0.63 % (3669861)Termination reason: Instruction limit
% 2.46/0.63 % (3669861)Termination phase: Saturation
% 2.46/0.63 % (3669861)Time elapsed: 0.113 s
% 2.46/0.63 % (3669861)Peak memory usage: 13 MB
% 2.46/0.63 % (3669861)Instructions burned: 159 (million)
% 2.46/0.63 % (3669879)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=67789375:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.46/0.63 % (3669880)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1319071292:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.46/0.63 % (3669873)Instruction limit reached!
% 2.46/0.63 % (3669873)------------------------------
% 2.46/0.63 % (3669873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.63 % (3669873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.63 % (3669873)CaDiCaL version: 2.1.3
% 2.46/0.63 % (3669873)Termination reason: Instruction limit
% 2.46/0.63 % (3669873)Termination phase: Saturation
% 2.46/0.63 % (3669873)Time elapsed: 0.083 s
% 2.46/0.63 % (3669873)Peak memory usage: 14 MB
% 2.46/0.63 % (3669873)Instructions burned: 182 (million)
% 2.46/0.63 % (3669883)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3218858153:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.46/0.63 % Exception at run slice level
% 2.46/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.46/0.63 % (3669874)Instruction limit reached!
% 2.46/0.63 % (3669874)------------------------------
% 2.46/0.63 % (3669874)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.63 % (3669874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.63 % (3669874)CaDiCaL version: 2.1.3
% 2.46/0.63 % (3669874)Termination reason: Instruction limit
% 2.46/0.63 % (3669874)Termination phase: Saturation
% 2.46/0.63 % (3669874)Time elapsed: 0.133 s
% 2.46/0.63 % (3669874)Peak memory usage: 15 MB
% 2.46/0.63 % (3669874)Instructions burned: 477 (million)
% 2.46/0.63 % (3669886)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=291224305:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.46/0.63 % (3669885)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=526485137: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)
% 2.46/0.63 % (3669886)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.46/0.63 % Exception at run slice level
% 2.46/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.46/0.63 % (3669885)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.46/0.63 % (3669889)fmb+10_1_sil=64000:random_seed=227914755:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 2.46/0.63 % (3669889)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 2.46/0.63 % Exception at run slice level
% 2.46/0.63 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.46/0.63 % (3669891)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2594633042:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 2.46/0.63 % (3669885) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3669850-3669885"...
% 2.46/0.63 % (3669885)...printing done.
% 2.46/0.63 % (3669885)Refutation found. Thanks to Tanya!
% 2.46/0.63 % SZS status Theorem for theBenchmark
% 2.46/0.63 % SZS output start Proof for theBenchmark
% 2.46/0.63 thf(type_def_5, type, denotational_interp: $tType).
% 2.46/0.63 thf(type_def_6, type, product_unit: $tType).
% 2.46/0.63 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 2.46/0.63 thf(type_def_8, type, variable: $tType).
% 2.46/0.63 thf(type_def_9, type, char: $tType).
% 2.46/0.63 thf(type_def_10, type, real: $tType).
% 2.46/0.63 thf(type_def_11, type, set: $tType > $tType).
% 2.46/0.63 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 2.46/0.63 thf(func_def_0, type, bNF_Gr: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > set @ product_prod @ X0 @ X1))).
% 2.46/0.63 thf(func_def_1, type, denotational_Consts: (denotational_interp > char > real)).
% 2.46/0.63 thf(func_def_2, type, denotational_Funcs: (denotational_interp > char > real > real)).
% 2.46/0.63 thf(func_def_3, type, denotational_Games: (denotational_interp > char > set @ (variable > real) > set @ (variable > real))).
% 2.46/0.63 thf(func_def_4, type, denotational_Preds: (denotational_interp > char > real > $o)).
% 2.46/0.63 thf(func_def_5, type, denota1150374853interp: (product_prod @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) > denotational_interp)).
% 2.46/0.63 thf(func_def_6, type, denotational_worlds: set @ (variable > real)).
% 2.46/0.63 thf(func_def_7, type, fun_reduction_pair: !>[X0: $tType]:((product_prod @ set @ product_prod @ X0 @ X0 @ set @ product_prod @ X0 @ X0 > $o))).
% 2.46/0.63 thf(func_def_8, type, fun_rp_inv_image: !>[X0: $tType, X1: $tType]:((product_prod @ set @ product_prod @ X0 @ X0 @ set @ product_prod @ X0 @ X0 > (X1 > X0) > product_prod @ set @ product_prod @ X1 @ X1 @ set @ product_prod @ X1 @ X1))).
% 2.46/0.63 thf(func_def_9, type, the: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_10, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 2.46/0.63 thf(func_def_11, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_12, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.46/0.63 thf(func_def_13, type, order_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 2.46/0.63 thf(func_def_14, type, top_top: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_15, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 2.46/0.63 thf(func_def_16, type, product_Pair_Rep: !>[X0: $tType, X1: $tType]:((X0 > X1 > X0 > X1 > $o))).
% 2.46/0.63 thf(func_def_17, type, product_Sigma: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > set @ X1) > set @ product_prod @ X0 @ X1))).
% 2.46/0.63 thf(func_def_18, type, product_curry: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X0 @ X1 > X2) > X0 > X1 > X2))).
% 2.46/0.63 thf(func_def_19, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.46/0.63 thf(func_def_20, type, product_map_prod: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > product_prod @ X0 @ X2 > product_prod @ X1 @ X3))).
% 2.46/0.63 thf(func_def_21, type, product_rec_bool: !>[X0: $tType]:((X0 > X0 > $o > X0))).
% 2.46/0.63 thf(func_def_22, type, product_rec_set_bool: !>[X0: $tType]:((X0 > X0 > $o > X0 > $o))).
% 2.46/0.63 thf(func_def_23, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.46/0.63 thf(func_def_24, type, product_rec_set_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2 > $o))).
% 2.46/0.63 thf(func_def_25, type, product_rec_set_unit: !>[X0: $tType]:((X0 > product_unit > X0 > $o))).
% 2.46/0.63 thf(func_def_26, type, product_rec_unit: !>[X0: $tType]:((X0 > product_unit > X0))).
% 2.46/0.63 thf(func_def_27, type, product_Abs_prod: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > product_prod @ X0 @ X1))).
% 2.46/0.63 thf(func_def_28, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 2.46/0.63 thf(func_def_29, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.46/0.63 thf(func_def_30, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.46/0.63 thf(func_def_31, type, product_swap: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > product_prod @ X1 @ X0))).
% 2.46/0.63 thf(func_def_32, type, product_product: !>[X0: $tType, X1: $tType]:((set @ X0 > set @ X1 > set @ product_prod @ X0 @ X1))).
% 2.46/0.63 thf(func_def_33, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 2.46/0.63 thf(func_def_34, type, inv_imagep: !>[X0: $tType, X1: $tType]:(((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o))).
% 2.46/0.63 thf(func_def_35, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 2.46/0.63 thf(func_def_36, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 2.46/0.63 thf(func_def_37, type, the_elem: !>[X0: $tType]:((set @ X0 > X0))).
% 2.46/0.63 thf(func_def_38, type, uSubst761942615e_repc: (denotational_interp > char > real > denotational_interp)).
% 2.46/0.63 thf(func_def_39, type, lex_prod: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > set @ product_prod @ X1 @ X1 > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 2.46/0.63 thf(func_def_40, type, same_fst: !>[X0: $tType, X1: $tType]:(((X0 > $o) > (X0 > set @ product_prod @ X1 @ X1) > set @ product_prod @ product_prod @ X0 @ X1 @ product_prod @ X0 @ X1))).
% 2.46/0.63 thf(func_def_41, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 2.46/0.63 thf(func_def_42, type, i: denotational_interp).
% 2.46/0.63 thf(func_def_43, type, d: real).
% 2.46/0.63 thf(func_def_44, type, f: char).
% 2.46/0.63 thf(func_def_46, type, vAND: ($o > $o > $o)).
% 2.46/0.63 thf(func_def_47, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 2.46/0.63 thf(func_def_48, type, db2: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_49, type, db0: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_51, type, db3: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.46/0.63 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.46/0.63 thf(func_def_56, type, vIMP: ($o > $o > $o)).
% 2.46/0.63 thf(func_def_57, type, vNOT: ($o > $o)).
% 2.46/0.63 thf(func_def_58, type, db4: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_59, type, db5: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_60, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.46/0.63 thf(func_def_61, type, vOR: ($o > $o > $o)).
% 2.46/0.63 thf(func_def_62, type, sP0: !>[X0: $tType]:(((X0 > $o) > X0 > $o))).
% 2.46/0.63 thf(func_def_63, type, sP1: !>[X0: $tType]:(((X0 > $o) > $o))).
% 2.46/0.63 thf(func_def_64, type, sP2: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > X1 > product_prod @ X1 @ X0 > $o))).
% 2.46/0.63 thf(func_def_65, type, sP3: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > $o))).
% 2.46/0.63 thf(func_def_66, type, sP4: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1 > $o))).
% 2.46/0.63 thf(func_def_67, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0))).
% 2.46/0.63 thf(func_def_68, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1))).
% 2.46/0.63 thf(func_def_69, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2))).
% 2.46/0.63 thf(func_def_70, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3))).
% 2.46/0.63 thf(func_def_71, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0))).
% 2.46/0.63 thf(func_def_72, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1))).
% 2.46/0.63 thf(func_def_73, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2))).
% 2.46/0.63 thf(func_def_74, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3))).
% 2.46/0.63 thf(func_def_75, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4))).
% 2.46/0.63 thf(func_def_76, type, sK14: !>[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))).
% 2.46/0.63 thf(func_def_77, type, sK15: !>[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))).
% 2.46/0.63 thf(func_def_78, type, sK16: !>[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))).
% 2.46/0.63 thf(func_def_79, type, sK17: !>[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))).
% 2.46/0.63 thf(func_def_80, type, sK18: !>[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))).
% 2.46/0.63 thf(func_def_81, type, sK19: !>[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))).
% 2.46/0.63 thf(func_def_82, type, sK20: !>[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))).
% 2.46/0.63 thf(func_def_83, type, sK21: !>[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))).
% 2.46/0.63 thf(func_def_84, type, sK22: !>[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))).
% 2.46/0.63 thf(func_def_85, type, sK23: !>[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))).
% 2.46/0.63 thf(func_def_86, type, sK24: !>[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))).
% 2.46/0.63 thf(func_def_87, type, sK25: !>[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))).
% 2.46/0.63 thf(func_def_88, type, sK26: !>[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))).
% 2.46/0.63 thf(func_def_89, type, sK27: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3))).
% 2.46/0.63 thf(func_def_90, type, sK28: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.46/0.63 thf(func_def_91, type, sK29: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.46/0.63 thf(func_def_92, type, sK30: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_93, 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) > X4))).
% 2.46/0.63 thf(func_def_94, 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) > X3))).
% 2.46/0.63 thf(func_def_95, type, sK33: !>[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))).
% 2.46/0.63 thf(func_def_96, type, sK34: !>[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))).
% 2.46/0.63 thf(func_def_97, type, sK35: !>[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))).
% 2.46/0.63 thf(func_def_98, type, sK36: !>[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))).
% 2.46/0.63 thf(func_def_99, type, sK37: !>[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))).
% 2.46/0.63 thf(func_def_100, type, sK38: !>[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))).
% 2.46/0.63 thf(func_def_101, type, sK39: !>[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))).
% 2.46/0.63 thf(func_def_102, type, sK40: !>[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))).
% 2.46/0.63 thf(func_def_103, type, sK41: !>[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))).
% 2.46/0.63 thf(func_def_104, type, sK42: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.46/0.63 thf(func_def_105, type, sK43: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_106, type, sK44: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.46/0.63 thf(func_def_107, type, sK45: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.46/0.63 thf(func_def_108, type, sK46: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X1))).
% 2.46/0.63 thf(func_def_109, type, sK47: !>[X0: $tType, X1: $tType]:(((product_prod @ X1 @ X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_110, type, sK48: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 2.46/0.63 thf(func_def_111, type, sK49: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 2.46/0.63 thf(func_def_112, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2))).
% 2.46/0.63 thf(func_def_113, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1))).
% 2.46/0.63 thf(func_def_114, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_115, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X0))).
% 2.46/0.63 thf(func_def_116, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X1))).
% 2.46/0.63 thf(func_def_117, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ product_prod @ X1 @ X2 > X2))).
% 2.46/0.63 thf(func_def_118, type, sK56: !>[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))).
% 2.46/0.63 thf(func_def_119, type, sK57: !>[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))).
% 2.46/0.63 thf(func_def_120, type, sK58: !>[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))).
% 2.46/0.63 thf(func_def_121, type, sK59: !>[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))).
% 2.46/0.63 thf(func_def_122, type, sK60: !>[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))).
% 2.46/0.63 thf(func_def_123, type, sK61: !>[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))).
% 2.46/0.63 thf(func_def_124, type, sK62: !>[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))).
% 2.46/0.63 thf(func_def_125, type, sK63: ((char > set @ (variable > real) > set @ (variable > real)) > char)).
% 2.46/0.63 thf(func_def_126, type, sK64: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_127, type, sK65: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 2.46/0.63 thf(func_def_128, type, sK66: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1))).
% 2.46/0.63 thf(func_def_129, type, sK67: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0))).
% 2.46/0.63 thf(func_def_130, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X2))).
% 2.46/0.63 thf(func_def_131, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X1))).
% 2.46/0.63 thf(func_def_132, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0))).
% 2.46/0.63 thf(func_def_133, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1))).
% 2.46/0.63 thf(func_def_134, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0))).
% 2.46/0.63 thf(func_def_135, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2))).
% 2.46/0.63 thf(func_def_136, type, sK74: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0))).
% 2.46/0.63 thf(func_def_137, type, sK75: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1))).
% 2.46/0.63 thf(func_def_138, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1))).
% 2.46/0.63 thf(func_def_139, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0))).
% 2.46/0.63 thf(func_def_140, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2))).
% 2.46/0.63 thf(func_def_141, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1))).
% 2.46/0.63 thf(func_def_142, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0))).
% 2.46/0.63 thf(func_def_143, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2))).
% 2.46/0.63 thf(func_def_144, type, sK82: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_145, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X2))).
% 2.46/0.63 thf(func_def_146, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X2 > X1 > X0) > product_prod @ X2 @ X1 > X1))).
% 2.46/0.63 thf(func_def_147, type, sK85: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_148, type, sK86: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 2.46/0.63 thf(func_def_149, type, sK87: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_150, type, sK88: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 2.46/0.63 thf(func_def_151, type, sK89: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 2.46/0.63 thf(func_def_152, type, sK90: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_153, type, sK91: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_154, type, sK92: !>[X0: $tType]:(((X0 > $o) > X0 > X0))).
% 2.46/0.63 thf(func_def_155, type, sK93: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_156, type, sK94: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_157, type, sK95: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_158, type, sK96: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_159, type, sK97: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_160, type, sK98: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_161, type, sK99: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > X1 > product_prod @ X1 @ X0 > X0))).
% 2.46/0.63 thf(func_def_162, type, sK100: !>[X0: $tType, X1: $tType]:(((X0 > set @ X1) > set @ X0 > product_prod @ X0 @ X1 > X0))).
% 2.46/0.63 thf(func_def_163, type, sK101: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_164, type, sK102: !>[X0: $tType]:((set @ X0 > X0))).
% 2.46/0.63 thf(func_def_165, type, sK103: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_166, type, sK104: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 2.46/0.63 thf(func_def_167, type, sK105: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 2.46/0.63 thf(func_def_168, type, sK106: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.46/0.63 thf(func_def_169, type, sK107: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 2.46/0.63 thf(func_def_170, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X3))).
% 2.46/0.63 thf(func_def_171, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((set @ product_prod @ X3 @ X2 > (X2 > X0) > (X3 > X1) > product_prod @ X1 @ X0 > X2))).
% 2.46/0.63 thf(func_def_172, type, sK110: !>[X0: $tType]:((set @ X0 > X0))).
% 2.46/0.63 thf(func_def_173, type, sK111: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X2))).
% 2.46/0.63 thf(func_def_174, type, sK112: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X1))).
% 2.46/0.63 thf(func_def_175, type, sK113: !>[X0: $tType, X1: $tType]:((X1 > (X1 > X0) > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_176, type, sK114: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 2.46/0.63 thf(func_def_177, type, sK115: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 2.46/0.63 thf(func_def_178, type, sK116: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 2.46/0.63 thf(func_def_179, type, sK117: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_180, type, sK118: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 2.46/0.63 thf(func_def_181, type, sK119: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 2.46/0.63 thf(func_def_182, type, sK120: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_183, type, sK121: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_184, type, sK122: !>[X0: $tType]:((set @ X0 > (X0 > $o) > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_185, type, sK123: !>[X0: $tType]:((set @ X0 > X0))).
% 2.46/0.63 thf(func_def_186, type, sK124: !>[X0: $tType, X1: $tType]:((set @ X0 > (X1 > X0 > $o) > (X1 > X0 > $o) > X1 > X0))).
% 2.46/0.63 thf(func_def_187, type, sK125: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > set @ X0 > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_188, type, sK126: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 2.46/0.63 thf(func_def_189, type, sK127: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > X1))).
% 2.46/0.63 thf(func_def_190, type, sK128: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 2.46/0.63 thf(func_def_191, type, sK129: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_192, type, sK130: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0 > X1))).
% 2.46/0.63 thf(func_def_193, type, sK131: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > X0 > X1))).
% 2.46/0.63 thf(func_def_194, type, sK132: !>[X0: $tType]:((set @ X0 > X0))).
% 2.46/0.63 thf(func_def_195, type, sK133: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > X1))).
% 2.46/0.63 thf(func_def_196, type, sK134: !>[X0: $tType]:((set @ X0 > X0))).
% 2.46/0.63 thf(func_def_197, type, sK135: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_198, type, sK136: !>[X0: $tType]:(((X0 > $o) > X0))).
% 2.46/0.63 thf(func_def_199, type, db6: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_200, type, sK137: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 2.46/0.63 thf(func_def_201, type, sK138: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 2.46/0.63 thf(func_def_202, type, db7: !>[X0: $tType]:(X0)).
% 2.46/0.63 thf(func_def_203, type, sK139: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 2.46/0.63 thf(f1,axiom,(
% 2.46/0.63 ! [X5 : (char > real),X6 : (char > real > real),X7 : (char > real > $o),X8 : (char > set @ (variable > real) > set @ (variable > real))] : (((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X5 @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X6 @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X7 @ X8)))))) = X7)),
% 2.46/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_Preds__mkinterp)).
% 2.46/0.63 thf(f35,axiom,(
% 2.46/0.63 ! [X0 : $tType,X1 : $tType] : (product_Pair_Rep @ X1 @ X0 = (^[X2 : X1, X3 : X0, X4 : X1, X5 : X0] : ((X5 = X3) & (X4 = X2))))),
% 2.46/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_Pair__Rep__def)).
% 2.46/0.63 thf(f40,axiom,(
% 2.46/0.63 ! [X0 : $tType,X1 : $tType] : (product_Pair @ X1 @ X0 = (^[X2 : X1, X3 : X0] : ((product_Abs_prod @ X1 @ X0 @ (product_Pair_Rep @ X1 @ X0 @ X2 @ X3)))))),
% 2.46/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Pair__def)).
% 2.46/0.63 thf(f97,axiom,(
% 2.46/0.63 ! [X0 : $tType] : (if @ X0 = (^[X1 : $o, X2 : X0, X3 : X0] : ((the @ X0 @ (^[X4 : X0] : ((~X1 => (X4 = X3)) & (X1 => (X4 = X2))))))))),
% 2.46/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_If__def)).
% 2.46/0.63 thf(f260,conjecture,(
% 2.46/0.63 (((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[X0 : char] : ((if @ real @ (X0 = f) @ d @ (denotational_Consts @ i @ X0)))) @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Funcs @ i) @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Preds @ i) @ (denotational_Games @ i))))))) = ((denotational_Preds @ i)))),
% 2.46/0.63 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 2.46/0.63 thf(f261,negated_conjecture,(
% 2.46/0.63 ~ (((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[X0 : char] : ((if @ real @ (X0 = f) @ d @ (denotational_Consts @ i @ X0)))) @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Funcs @ i) @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Preds @ i) @ (denotational_Games @ i))))))) = ((denotational_Preds @ i)))),
% 2.46/0.63 inference(negated_conjecture,[status(cth)],[f260])).
% 2.46/0.63 thf(f293,plain,(
% 2.46/0.63 ! [X0 : $tType,X1 : $tType] : (product_Pair_Rep @ X1 @ X0 = (^[Y0 : X1]: ((^[Y1 : X0]: ((^[Y2 : X1]: ((^[Y3 : X0]: ((Y0 = Y2) & (Y1 = Y3))))))))))),
% 2.46/0.63 inference(fool_elimination,[],[f35])).
% 2.46/0.63 thf(f300,plain,(
% 2.46/0.63 ! [X0 : $tType,X1 : $tType] : (product_Pair @ X1 @ X0 = (^[Y0 : X1]: ((^[Y1 : X0]: (product_Abs_prod @ X1 @ X0 @ (product_Pair_Rep @ X1 @ X0 @ Y0 @ Y1))))))),
% 2.46/0.63 inference(fool_elimination,[],[f40])).
% 2.46/0.63 thf(f385,plain,(
% 2.46/0.63 ! [X0 : $tType] : (if @ X0 = (^[X1 : $o, X2 : X0, X3 : X0] : ((the @ X0 @ (^[X4 : X0] : ((~X1 => (X4 = X3)) & (X1 => (X4 = X2))))))))),
% 2.46/0.63 inference(rectify,[],[f97])).
% 2.46/0.63 thf(f386,plain,(
% 2.46/0.63 ! [X0 : $tType] : (if @ X0 = (^[Y0 : $o]: ((^[Y1 : X0]: ((^[Y2 : X0]: (the @ X0 @ (^[Y3 : X0]: ((Y0 => (Y1 = Y3)) & ((~ Y0) => (Y2 = Y3)))))))))))),
% 2.46/0.63 inference(fool_elimination,[],[f385])).
% 2.46/0.63 thf(f639,plain,(
% 2.46/0.63 ~ (((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[X0 : char] : ((if @ real @ (X0 = f) @ d @ (denotational_Consts @ i @ X0)))) @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Funcs @ i) @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Preds @ i) @ (denotational_Games @ i))))))) = ((denotational_Preds @ i)))),
% 2.46/0.63 inference(rectify,[],[f261])).
% 2.46/0.63 thf(f640,plain,(
% 2.46/0.63 ~ (((denotational_Preds @ i)) = ((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y0 : char]: (if @ real @ (f = Y0) @ d @ (denotational_Consts @ i @ Y0))) @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Funcs @ i) @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Preds @ i) @ (denotational_Games @ i))))))))),
% 2.46/0.63 inference(fool_elimination,[],[f639])).
% 2.46/0.63 thf(f641,plain,(
% 2.46/0.63 ! [X0 : (char > real),X1 : (char > real > real),X2 : (char > real > $o),X3 : (char > set @ (variable > real) > set @ (variable > real))] : (((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X0 @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X1 @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X2 @ X3)))))) = X2)),
% 2.46/0.64 inference(rectify,[],[f1])).
% 2.46/0.64 thf(f657,plain,(
% 2.46/0.64 (((denotational_Preds @ i)) != ((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y0 : char]: (if @ real @ (f = Y0) @ d @ (denotational_Consts @ i @ Y0))) @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Funcs @ i) @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Preds @ i) @ (denotational_Games @ i))))))))),
% 2.46/0.64 inference(flattening,[],[f640])).
% 2.46/0.64 thf(f896,plain,(
% 2.46/0.64 ( ! [X2 : (char > real > $o),X3 : (char > set @ (variable > real) > set @ (variable > real)),X0 : (char > real),X1 : (char > real > real)] : ((((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X0 @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X1 @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ X2 @ X3)))))) = X2)) )),
% 2.46/0.64 inference(cnf_transformation,[],[f641])).
% 2.46/0.64 thf(f932,plain,(
% 2.46/0.64 ( ! [X1 : $tType,X0 : $tType] : ((product_Pair_Rep @ X1 @ X0 = (^[Y0 : X1]: ((^[Y1 : X0]: ((^[Y2 : X1]: ((^[Y3 : X0]: ((Y0 = Y2) & (Y1 = Y3))))))))))) )),
% 2.46/0.64 inference(cnf_transformation,[],[f293])).
% 2.46/0.64 thf(f937,plain,(
% 2.46/0.64 ( ! [X1 : $tType,X0 : $tType] : ((product_Pair @ X1 @ X0 = (^[Y0 : X1]: ((^[Y1 : X0]: (product_Abs_prod @ X1 @ X0 @ (product_Pair_Rep @ X1 @ X0 @ Y0 @ Y1))))))) )),
% 2.46/0.64 inference(cnf_transformation,[],[f300])).
% 2.46/0.64 thf(f1013,plain,(
% 2.46/0.64 ( ! [X0 : $tType] : ((if @ X0 = (^[Y0 : $o]: ((^[Y1 : X0]: ((^[Y2 : X0]: (the @ X0 @ (^[Y3 : X0]: ((Y0 => (Y1 = Y3)) & ((~ Y0) => (Y2 = Y3)))))))))))) )),
% 2.46/0.64 inference(cnf_transformation,[],[f386])).
% 2.46/0.64 thf(f1210,plain,(
% 2.46/0.64 (((denotational_Preds @ i)) != ((denotational_Preds @ (denota1150374853interp @ (product_Pair @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y0 : char]: (if @ real @ (f = Y0) @ d @ (denotational_Consts @ i @ Y0))) @ (product_Pair @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Funcs @ i) @ (product_Pair @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (denotational_Preds @ i) @ (denotational_Games @ i))))))))),
% 2.46/0.64 inference(cnf_transformation,[],[f657])).
% 2.46/0.64 thf(f1213,plain,(
% 2.46/0.64 ( ! [X1 : $tType,X0 : $tType] : ((product_Pair @ X1 @ X0 = (^[Y0 : X1]: ((^[Y1 : X0]: (product_Abs_prod @ X1 @ X0 @ ((^[Y2 : X1]: ((^[Y3 : X0]: ((^[Y4 : X1]: ((^[Y5 : X0]: ((Y2 = Y4) & (Y3 = Y5))))))))) @ Y0 @ Y1))))))) )),
% 2.46/0.64 inference(definition_unfolding,[],[f937,f932])).
% 2.46/0.64 thf(f1223,plain,(
% 2.46/0.64 ( ! [X2 : (char > real > $o),X3 : (char > set @ (variable > real) > set @ (variable > real)),X0 : (char > real),X1 : (char > real > real)] : ((((denotational_Preds @ (denota1150374853interp @ ((^[Y0 : char > real]: ((^[Y1 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: (product_Abs_prod @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ ((^[Y2 : char > real]: ((^[Y3 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((^[Y4 : char > real]: ((^[Y5 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((Y2 = Y4) & (Y3 = Y5))))))))) @ Y0 @ Y1))))) @ X0 @ ((^[Y0 : char > real > real]: ((^[Y1 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: (product_Abs_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ ((^[Y2 : char > real > real]: ((^[Y3 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((^[Y4 : char > real > real]: ((^[Y5 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((Y2 = Y4) & (Y3 = Y5))))))))) @ Y0 @ Y1))))) @ X1 @ ((^[Y0 : char > real > $o]: ((^[Y1 : char > set @ (variable > real) > set @ (variable > real)]: (product_Abs_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ ((^[Y2 : char > real > $o]: ((^[Y3 : char > set @ (variable > real) > set @ (variable > real)]: ((^[Y4 : char > real > $o]: ((^[Y5 : char > set @ (variable > real) > set @ (variable > real)]: ((Y2 = Y4) & (Y3 = Y5))))))))) @ Y0 @ Y1))))) @ X2 @ X3)))))) = X2)) )),
% 2.46/0.64 inference(definition_unfolding,[],[f896,f1213,f1213,f1213])).
% 2.46/0.64 thf(f1357,plain,(
% 2.46/0.64 (((denotational_Preds @ i)) != ((denotational_Preds @ (denota1150374853interp @ ((^[Y0 : char > real]: ((^[Y1 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: (product_Abs_prod @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ ((^[Y2 : char > real]: ((^[Y3 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((^[Y4 : char > real]: ((^[Y5 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((Y2 = Y4) & (Y3 = Y5))))))))) @ Y0 @ Y1))))) @ (^[Y0 : char]: ((^[Y1 : $o]: ((^[Y2 : real]: ((^[Y3 : real]: (the @ real @ (^[Y4 : real]: ((Y1 => (Y2 = Y4)) & ((~ Y1) => (Y3 = Y4)))))))))) @ (f = Y0) @ d @ (denotational_Consts @ i @ Y0))) @ ((^[Y0 : char > real > real]: ((^[Y1 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: (product_Abs_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ ((^[Y2 : char > real > real]: ((^[Y3 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((^[Y4 : char > real > real]: ((^[Y5 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((Y2 = Y4) & (Y3 = Y5))))))))) @ Y0 @ Y1))))) @ (denotational_Funcs @ i) @ ((^[Y0 : char > real > $o]: ((^[Y1 : char > set @ (variable > real) > set @ (variable > real)]: (product_Abs_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ ((^[Y2 : char > real > $o]: ((^[Y3 : char > set @ (variable > real) > set @ (variable > real)]: ((^[Y4 : char > real > $o]: ((^[Y5 : char > set @ (variable > real) > set @ (variable > real)]: ((Y2 = Y4) & (Y3 = Y5))))))))) @ Y0 @ Y1))))) @ (denotational_Preds @ i) @ (denotational_Games @ i))))))))),
% 2.46/0.64 inference(definition_unfolding,[],[f1210,f1213,f1013,f1213,f1213])).
% 2.46/0.64 thf(f1395,plain,(
% 2.46/0.64 (((denotational_Preds @ i)) != ((denotational_Preds @ (denota1150374853interp @ (product_Abs_prod @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y0 : char > real]: ((^[Y1 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: (((^[Y2 : char]: (the @ real @ (^[Y3 : real]: (((f = Y2) => (d = Y3)) & ((~ (f = Y2)) => ((denotational_Consts @ i @ Y2) = Y3)))))) = Y0) & ((product_Abs_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y2 : char > real > real]: ((^[Y3 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: (((denotational_Funcs @ i) = Y2) & ((product_Abs_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y4 : char > real > $o]: ((^[Y5 : char > set @ (variable > real) > set @ (variable > real)]: (((denotational_Preds @ i) = Y4) & ((denotational_Games @ i) = Y5)))))) = Y3)))))) = Y1))))))))))),
% 2.46/0.64 inference(beta-eta_normalization,[],[f1357])).
% 2.46/0.64 thf(f1877,plain,(
% 2.46/0.64 ( ! [X2 : (char > real > $o),X3 : (char > set @ (variable > real) > set @ (variable > real)),X0 : (char > real),X1 : (char > real > real)] : ((((denotational_Preds @ (denota1150374853interp @ (product_Abs_prod @ (char > real) @ product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y0 : char > real]: ((^[Y1 : product_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((X0 = Y0) & ((product_Abs_prod @ (char > real > real) @ product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y2 : char > real > real]: ((^[Y3 : product_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real))]: ((X1 = Y2) & ((product_Abs_prod @ (char > real > $o) @ (char > set @ (variable > real) > set @ (variable > real)) @ (^[Y4 : char > real > $o]: ((^[Y5 : char > set @ (variable > real) > set @ (variable > real)]: ((X2 = Y4) & (X3 = Y5)))))) = Y3)))))) = Y1))))))))) = X2)) )),
% 2.46/0.64 inference(beta-eta_normalization,[],[f1223])).
% 2.46/0.64 thf(f1889,plain,(
% 2.46/0.64 $false),
% 2.46/0.64 inference(backward_subsumption_resolution,[],[f1395,f1877])).
% 2.46/0.64 % SZS output end Proof for theBenchmark
% 2.46/0.64 % (3669885)------------------------------
% 2.46/0.64 % (3669885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.64 % (3669885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.64 % (3669885)CaDiCaL version: 2.1.3
% 2.46/0.64 % (3669885)Termination reason: Refutation
% 2.46/0.64 % (3669885)Time elapsed: 0.133 s
% 2.46/0.64 % (3669885)Peak memory usage: 16 MB
% 2.46/0.64 % (3669885)Instructions burned: 237 (million)
% 2.46/0.64 % (3669850)Success in time 0.409 s
% 2.46/0.64 % Vampire exiting
%------------------------------------------------------------------------------