%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP113^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 08:10:44 AM UTC 2026
% Result : Theorem 0.56s 0.31s
% Output : Refutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP113^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 19:55:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.12 Running first-order model finding
% 0.08/0.12 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.56/0.31 % (605891)Will run a generic schedule for satisfiability detection.
% 0.56/0.31 % (605897)% WARNING: option uhcvi not known.
% 0.56/0.31 % (605897)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4086445268:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.56/0.31 % (605896)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2283851712_2999 on theBenchmark for (2999ds/0Mi)
% 0.56/0.31 % (605899)dis+10_1_sil=32000:sp=arity:random_seed=1695520503:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.56/0.31 % (605898)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3878684820:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.56/0.31 % (605901)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=262537502:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.56/0.31 % (605900)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3300948345:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.56/0.31 % (605902)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=129995524:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.56/0.31 % (605897)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.56/0.31 % (605900)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.56/0.31 % (605899)Instruction limit reached!
% 0.56/0.31 % (605899)------------------------------
% 0.56/0.31 % (605899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.31 % (605899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.31 % (605899)CaDiCaL version: 2.1.3
% 0.56/0.31 % (605899)Termination reason: Instruction limit
% 0.56/0.31 % (605899)Termination phase: Property scanning
% 0.56/0.31 % (605899)Time elapsed: 0.022 s
% 0.56/0.31 % (605899)Peak memory usage: 11 MB
% 0.56/0.31 % (605899)Instructions burned: 103 (million)
% 0.56/0.31 % Exception at run slice level
% 0.56/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.56/0.31 % (605897)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.56/0.31 % (605900)Instruction limit reached!
% 0.56/0.31 % (605900)------------------------------
% 0.56/0.31 % (605900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.31 % (605900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.31 % (605900)CaDiCaL version: 2.1.3
% 0.56/0.31 % (605900)Termination reason: Instruction limit
% 0.56/0.31 % (605900)Termination phase: Saturation
% 0.56/0.31 % (605900)Time elapsed: 0.026 s
% 0.56/0.31 % (605900)Peak memory usage: 12 MB
% 0.56/0.31 % (605900)Instructions burned: 119 (million)
% 0.56/0.31 % (605901)Instruction limit reached!
% 0.56/0.31 % (605901)------------------------------
% 0.56/0.31 % (605901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.31 % (605901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.31 % (605901)CaDiCaL version: 2.1.3
% 0.56/0.31 % (605901)Termination reason: Instruction limit
% 0.56/0.31 % (605901)Termination phase: Saturation
% 0.56/0.31 % (605901)Time elapsed: 0.030 s
% 0.56/0.31 % (605901)Peak memory usage: 13 MB
% 0.56/0.31 % (605901)Instructions burned: 134 (million)
% 0.56/0.31 % (605910)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1889058732:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.56/0.31 % (605911)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2808285801:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.56/0.31 % (605912)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=1879441875:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.56/0.31 % (605902)Instruction limit reached!
% 0.56/0.31 % (605902)------------------------------
% 0.56/0.31 % (605902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.31 % (605902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.31 % (605902)CaDiCaL version: 2.1.3
% 0.56/0.31 % (605902)Termination reason: Instruction limit
% 0.56/0.31 % (605902)Termination phase: Saturation
% 0.56/0.31 % (605902)Time elapsed: 0.037 s
% 0.56/0.31 % (605902)Peak memory usage: 13 MB
% 0.56/0.31 % (605902)Instructions burned: 162 (million)
% 0.56/0.31 % (605913)ott-21_1_sil=16000:fs=off:random_seed=3225748167:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.56/0.31 % (605912)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.56/0.31 % (605917)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3748920480:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.56/0.31 % Exception at run slice level
% 0.56/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.56/0.31 % (605912)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.56/0.31 % (605911)Instruction limit reached!
% 0.56/0.31 % (605911)------------------------------
% 0.56/0.31 % (605911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.31 % (605911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.31 % (605911)CaDiCaL version: 2.1.3
% 0.56/0.31 % (605911)Termination reason: Instruction limit
% 0.56/0.31 % (605911)Termination phase: Saturation
% 0.56/0.31 % (605911)Time elapsed: 0.029 s
% 0.56/0.31 % (605911)Peak memory usage: 13 MB
% 0.56/0.31 % (605911)Instructions burned: 132 (million)
% 0.56/0.31 % (605920)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2828350569:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.56/0.31 % (605921)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1678443381:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.56/0.31 % (605913)Instruction limit reached!
% 0.56/0.31 % (605913)------------------------------
% 0.56/0.31 % (605913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.31 % (605913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.31 % (605913)CaDiCaL version: 2.1.3
% 0.56/0.31 % (605913)Termination reason: Instruction limit
% 0.56/0.31 % (605913)Termination phase: Saturation
% 0.56/0.31 % (605913)Time elapsed: 0.041 s
% 0.56/0.31 % (605913)Peak memory usage: 13 MB
% 0.56/0.31 % (605913)Instructions burned: 183 (million)
% 0.56/0.31 % (605924)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3104886558:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.56/0.31 % Exception at run slice level
% 0.56/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.56/0.31 % (605926)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=4274401593:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 0.56/0.31 % (605926)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.56/0.31 % Exception at run slice level
% 0.56/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.56/0.31 % (605928)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3169478787:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 0.56/0.31 % (605928)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.56/0.31 % (605921) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-605891-605921"...
% 0.56/0.31 % (605921)...printing done.
% 0.56/0.31 % (605921)Refutation found. Thanks to Tanya!
% 0.56/0.31 % SZS status Theorem for theBenchmark
% 0.56/0.31 % SZS output start Proof for theBenchmark
% 0.56/0.31 thf(type_def_5, type, produc2021989178_set_a: $tType).
% 0.56/0.31 thf(type_def_6, type, produc211508562a_real: $tType).
% 0.56/0.31 thf(type_def_7, type, produc1312517202t_real: $tType).
% 0.56/0.31 thf(type_def_8, type, produc304417648_set_a: $tType).
% 0.56/0.31 thf(type_def_9, type, produc509513372a_real: $tType).
% 0.56/0.31 thf(type_def_10, type, produc25772804_set_a: $tType).
% 0.56/0.31 thf(type_def_11, type, set_Pr1158285382l_real: $tType).
% 0.56/0.31 thf(type_def_12, type, produc792423270l_real: $tType).
% 0.56/0.31 thf(type_def_13, type, produc1931999653t_real: $tType).
% 0.56/0.31 thf(type_def_14, type, produc232195311t_real: $tType).
% 0.56/0.31 thf(type_def_15, type, produc1350454001_set_a: $tType).
% 0.56/0.31 thf(type_def_16, type, set_Pr147102617l_real: $tType).
% 0.56/0.31 thf(type_def_17, type, produc1691597095_set_a: $tType).
% 0.56/0.31 thf(type_def_18, type, set_Pr1928503567a_real: $tType).
% 0.56/0.31 thf(type_def_19, type, produc957004601l_real: $tType).
% 0.56/0.31 thf(type_def_20, type, produc581916509al_nat: $tType).
% 0.56/0.31 thf(type_def_21, type, produc845587165t_real: $tType).
% 0.56/0.31 thf(type_def_22, type, product_prod_nat_nat: $tType).
% 0.56/0.31 thf(type_def_23, type, product_prod_a_real: $tType).
% 0.56/0.31 thf(type_def_24, type, set_real: $tType).
% 0.56/0.31 thf(type_def_25, type, extended_ereal: $tType).
% 0.56/0.31 thf(type_def_26, type, set_a: $tType).
% 0.56/0.31 thf(type_def_27, type, real: $tType).
% 0.56/0.31 thf(type_def_28, type, nat: $tType).
% 0.56/0.31 thf(type_def_29, type, a: $tType).
% 0.56/0.31 thf(type_def_30, type, sTfun: ($tType * $tType) > $tType).
% 0.56/0.31 thf(func_def_0, type, elemen1695521870a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real)).
% 0.56/0.31 thf(func_def_1, type, elemen1168706977e_real: (set_real > set_real)).
% 0.56/0.31 thf(func_def_2, type, elementary_closure_a: (set_a > set_a)).
% 0.56/0.31 thf(func_def_3, type, zero_zero_nat: nat).
% 0.56/0.31 thf(func_def_4, type, zero_zero_real: real).
% 0.56/0.31 thf(func_def_5, type, lower_870348689a_real: (set_Pr1928503567a_real > (product_prod_a_real > extended_ereal) > set_Pr1158285382l_real)).
% 0.56/0.31 thf(func_def_6, type, lower_1607476196h_real: (set_real > (real > extended_ereal) > set_Pr147102617l_real)).
% 0.56/0.31 thf(func_def_7, type, lower_930854854raph_a: (set_a > (a > extended_ereal) > set_Pr1928503567a_real)).
% 0.56/0.31 thf(func_def_8, type, ord_less_nat: (nat > nat > $o)).
% 0.56/0.31 thf(func_def_9, type, ord_le297355219_set_a: (produc1691597095_set_a > produc1691597095_set_a > $o)).
% 0.56/0.31 thf(func_def_10, type, ord_less_real: (real > real > $o)).
% 0.56/0.31 thf(func_def_11, type, ord_le1379034467a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real > $o)).
% 0.56/0.31 thf(func_def_12, type, ord_less_set_real: (set_real > set_real > $o)).
% 0.56/0.31 thf(func_def_13, type, ord_less_set_a: (set_a > set_a > $o)).
% 0.56/0.31 thf(func_def_14, type, ord_less_eq_nat: (nat > nat > $o)).
% 0.56/0.31 thf(func_def_15, type, ord_le1302190241at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o)).
% 0.56/0.31 thf(func_def_16, type, ord_le1950669437t_real: (produc845587165t_real > produc845587165t_real > $o)).
% 0.56/0.31 thf(func_def_17, type, ord_le1686998781al_nat: (produc581916509al_nat > produc581916509al_nat > $o)).
% 0.56/0.31 thf(func_def_18, type, ord_le1342644953l_real: (produc957004601l_real > produc957004601l_real > $o)).
% 0.56/0.31 thf(func_def_19, type, ord_le486764743_set_a: (produc1691597095_set_a > produc1691597095_set_a > $o)).
% 0.56/0.31 thf(func_def_20, type, ord_less_eq_real: (real > real > $o)).
% 0.56/0.31 thf(func_def_21, type, ord_le1586073967a_real: (set_Pr1928503567a_real > set_Pr1928503567a_real > $o)).
% 0.56/0.31 thf(func_def_22, type, ord_less_eq_set_real: (set_real > set_real > $o)).
% 0.56/0.31 thf(func_def_23, type, ord_less_eq_set_a: (set_a > set_a > $o)).
% 0.56/0.31 thf(func_def_24, type, top_to1567080838real_o: (product_prod_a_real > $o)).
% 0.56/0.31 thf(func_def_25, type, top_top_real_o: (real > $o)).
% 0.56/0.31 thf(func_def_26, type, top_top_a_o: (a > $o)).
% 0.56/0.31 thf(func_def_27, type, top_to991334818t_real: produc1312517202t_real).
% 0.56/0.31 thf(func_def_28, type, top_to345582004_set_a: produc25772804_set_a).
% 0.56/0.31 thf(func_def_29, type, top_to522338794_set_a: produc2021989178_set_a).
% 0.56/0.31 thf(func_def_30, type, top_to2037809826a_real: produc211508562a_real).
% 0.56/0.31 thf(func_def_31, type, top_to95743733t_real: produc1931999653t_real).
% 0.56/0.31 thf(func_def_32, type, top_to1153982881_set_a: produc1350454001_set_a).
% 0.56/0.31 thf(func_def_33, type, top_to724687040_set_a: produc304417648_set_a).
% 0.56/0.31 thf(func_def_34, type, top_to829322572a_real: produc509513372a_real).
% 0.56/0.31 thf(func_def_35, type, top_to35724191t_real: produc232195311t_real).
% 0.56/0.31 thf(func_def_36, type, top_to1477940855_set_a: produc1691597095_set_a).
% 0.56/0.31 thf(func_def_37, type, top_to2138011583a_real: set_Pr1928503567a_real).
% 0.56/0.31 thf(func_def_38, type, top_top_set_real: set_real).
% 0.56/0.31 thf(func_def_39, type, top_top_set_a: set_a).
% 0.56/0.31 thf(func_def_40, type, product_Pair_nat_nat: (nat > nat > product_prod_nat_nat)).
% 0.56/0.31 thf(func_def_41, type, produc49576085t_real: (nat > real > produc845587165t_real)).
% 0.56/0.31 thf(func_def_42, type, produc1214388894l_real: (product_prod_a_real > real > produc792423270l_real)).
% 0.56/0.31 thf(func_def_43, type, produc1541812501al_nat: (real > nat > produc581916509al_nat)).
% 0.56/0.31 thf(func_def_44, type, produc705216881l_real: (real > real > produc957004601l_real)).
% 0.56/0.31 thf(func_def_45, type, produc471223946t_real: (set_Pr1928503567a_real > set_real > produc1312517202t_real)).
% 0.56/0.31 thf(func_def_46, type, produc1220567734_set_a: (set_Pr1928503567a_real > set_a > produc25772804_set_a)).
% 0.56/0.31 thf(func_def_47, type, produc1162518380_set_a: (set_real > produc1691597095_set_a > produc2021989178_set_a)).
% 0.56/0.31 thf(func_def_48, type, produc150798858a_real: (set_real > set_Pr1928503567a_real > produc211508562a_real)).
% 0.56/0.31 thf(func_def_49, type, produc119681757t_real: (set_real > set_real > produc1931999653t_real)).
% 0.56/0.31 thf(func_def_50, type, produc190993315_set_a: (set_real > set_a > produc1350454001_set_a)).
% 0.56/0.31 thf(func_def_51, type, produc272677600_set_a: (set_a > produc1691597095_set_a > produc304417648_set_a)).
% 0.56/0.31 thf(func_def_52, type, produc383769494a_real: (set_a > set_Pr1928503567a_real > produc509513372a_real)).
% 0.56/0.31 thf(func_def_53, type, produc1266579561t_real: (set_a > set_real > produc232195311t_real)).
% 0.56/0.31 thf(func_def_54, type, produc1928581911_set_a: (set_a > set_a > produc1691597095_set_a)).
% 0.56/0.31 thf(func_def_55, type, product_Pair_a_real: (a > real > product_prod_a_real)).
% 0.56/0.31 thf(func_def_56, type, real_V404783528a_real: (product_prod_a_real > product_prod_a_real > real)).
% 0.56/0.31 thf(func_def_57, type, real_V1934908667t_real: (real > real > real)).
% 0.56/0.31 thf(func_def_58, type, real_V1514887919dist_a: (a > a > real)).
% 0.56/0.31 thf(func_def_59, type, collec1714955950a_real: ((product_prod_a_real > $o) > set_Pr1928503567a_real)).
% 0.56/0.31 thf(func_def_60, type, collect_real: ((real > $o) > set_real)).
% 0.56/0.31 thf(func_def_61, type, collect_a: ((a > $o) > set_a)).
% 0.56/0.31 thf(func_def_62, type, member565909519l_real: (produc792423270l_real > set_Pr1158285382l_real > $o)).
% 0.56/0.31 thf(func_def_63, type, member1068169442l_real: (produc957004601l_real > set_Pr147102617l_real > $o)).
% 0.56/0.31 thf(func_def_64, type, member1103263856a_real: (product_prod_a_real > set_Pr1928503567a_real > $o)).
% 0.56/0.31 thf(func_def_65, type, member_real: (real > set_real > $o)).
% 0.56/0.31 thf(func_def_66, type, member_a: (a > set_a > $o)).
% 0.56/0.31 thf(func_def_67, type, e: real).
% 0.56/0.31 thf(func_def_68, type, f: (a > extended_ereal)).
% 0.56/0.31 thf(func_def_69, type, thesis: $o).
% 0.56/0.31 thf(func_def_70, type, x: a).
% 0.56/0.31 thf(func_def_71, type, y: real).
% 0.56/0.31 thf(func_def_72, type, z: real).
% 0.56/0.31 thf(func_def_76, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.56/0.31 thf(func_def_77, type, vAND: ($o > $o > $o)).
% 0.56/0.32 thf(func_def_78, type, vNOT: ($o > $o)).
% 0.56/0.32 thf(func_def_79, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.56/0.32 thf(func_def_80, type, vIMP: ($o > $o > $o)).
% 0.56/0.32 thf(func_def_81, type, db0: !>[X0: $tType]:(X0)).
% 0.56/0.32 thf(func_def_82, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.56/0.32 thf(func_def_83, type, db1: !>[X0: $tType]:(X0)).
% 0.56/0.32 thf(func_def_84, type, vOR: ($o > $o > $o)).
% 0.56/0.32 thf(func_def_85, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.56/0.32 thf(func_def_86, type, db2: !>[X0: $tType]:(X0)).
% 0.56/0.32 thf(func_def_87, type, sP0: (real > real > real > $o)).
% 0.56/0.32 thf(func_def_88, type, sP1: (real > real > real > $o)).
% 0.56/0.32 thf(func_def_89, type, sP2: (real > real > real > $o)).
% 0.56/0.32 thf(func_def_90, type, sP3: (nat > nat > nat > $o)).
% 0.56/0.32 thf(func_def_91, type, sP4: (nat > nat > nat > $o)).
% 0.56/0.32 thf(func_def_92, type, sP5: (nat > nat > nat > $o)).
% 0.56/0.32 thf(func_def_93, type, sK6: product_prod_a_real).
% 0.56/0.32 thf(func_def_94, type, sK7: ((real > real) > real)).
% 0.56/0.32 thf(func_def_95, type, sK8: ((real > real) > real)).
% 0.56/0.32 thf(func_def_96, type, sK9: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_97, type, sK10: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_98, type, sK11: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_99, type, sK12: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_100, type, sK13: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_101, type, sK14: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_102, type, sK15: ((real > real) > real)).
% 0.56/0.32 thf(func_def_103, type, sK16: ((real > real) > real)).
% 0.56/0.32 thf(func_def_104, type, sK17: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_105, type, sK18: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_106, type, sK19: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_107, type, sK20: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_108, type, sK21: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_109, type, sK22: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_110, type, sK23: ((real > real) > real)).
% 0.56/0.32 thf(func_def_111, type, sK24: ((real > real) > real)).
% 0.56/0.32 thf(func_def_112, type, sK25: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_113, type, sK26: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_114, type, sK27: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_115, type, sK28: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_116, type, sK29: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_117, type, sK30: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_118, type, sK31: ((real > real) > real)).
% 0.56/0.32 thf(func_def_119, type, sK32: ((real > real) > real)).
% 0.56/0.32 thf(func_def_120, type, sK33: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_121, type, sK34: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_122, type, sK35: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_123, type, sK36: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_124, type, sK37: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_125, type, sK38: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_126, type, sK39: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_127, type, sK40: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_128, type, sK41: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_129, type, sK42: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_130, type, sK43: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_131, type, sK44: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_132, type, sK45: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_133, type, sK46: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_134, type, sK47: (real > real > real > real)).
% 0.56/0.32 thf(func_def_135, type, sK48: (real > real > real > real)).
% 0.56/0.32 thf(func_def_136, type, sK49: (real > real > real)).
% 0.56/0.32 thf(func_def_137, type, sK50: (real > real > real)).
% 0.56/0.32 thf(func_def_138, type, sK51: ((real > real) > real)).
% 0.56/0.32 thf(func_def_139, type, sK52: ((real > real) > real)).
% 0.56/0.32 thf(func_def_140, type, sK53: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_141, type, sK54: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_142, type, sK55: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_143, type, sK56: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_144, type, sK57: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_145, type, sK58: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_146, type, sK59: ((real > real) > real)).
% 0.56/0.32 thf(func_def_147, type, sK60: ((real > real) > real)).
% 0.56/0.32 thf(func_def_148, type, sK61: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_149, type, sK62: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_150, type, sK63: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_151, type, sK64: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_152, type, sK65: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_153, type, sK66: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_154, type, sK67: ((real > real) > real)).
% 0.56/0.32 thf(func_def_155, type, sK68: ((real > real) > real)).
% 0.56/0.32 thf(func_def_156, type, sK69: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_157, type, sK70: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_158, type, sK71: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_159, type, sK72: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_160, type, sK73: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_161, type, sK74: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_162, type, sK75: ((real > real) > real)).
% 0.56/0.32 thf(func_def_163, type, sK76: ((real > real) > real)).
% 0.56/0.32 thf(func_def_164, type, sK77: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_165, type, sK78: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_166, type, sK79: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_167, type, sK80: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_168, type, sK81: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_169, type, sK82: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_170, type, sK83: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_171, type, sK84: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_172, type, sK85: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_173, type, sK86: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_174, type, sK87: ((real > real > $o) > real)).
% 0.56/0.32 thf(func_def_175, type, sK88: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_176, type, sK89: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_177, type, sK90: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_178, type, sK91: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_179, type, sK92: ((nat > nat > $o) > nat)).
% 0.56/0.32 thf(func_def_180, type, sK93: ((nat > $o) > nat)).
% 0.56/0.32 thf(func_def_181, type, sK94: (real > real > real)).
% 0.56/0.32 thf(func_def_182, type, sK95: (real > real)).
% 0.56/0.32 thf(func_def_183, type, sK96: (nat > nat)).
% 0.56/0.32 thf(func_def_184, type, sK97: (real > real)).
% 0.56/0.32 thf(func_def_185, type, sK98: ((real > real) > real)).
% 0.56/0.32 thf(func_def_186, type, sK99: ((real > real) > real)).
% 0.56/0.32 thf(func_def_187, type, sK100: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_188, type, sK101: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_189, type, sK102: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_190, type, sK103: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_191, type, sK104: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_192, type, sK105: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_193, type, sK106: ((real > real) > real)).
% 0.56/0.32 thf(func_def_194, type, sK107: ((real > real) > real)).
% 0.56/0.32 thf(func_def_195, type, sK108: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_196, type, sK109: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_197, type, sK110: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_198, type, sK111: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_199, type, sK112: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_200, type, sK113: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_201, type, sK114: ((real > real) > real)).
% 0.56/0.32 thf(func_def_202, type, sK115: ((real > real) > real)).
% 0.56/0.32 thf(func_def_203, type, sK116: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_204, type, sK117: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_205, type, sK118: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_206, type, sK119: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_207, type, sK120: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_208, type, sK121: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_209, type, sK122: ((real > real) > real)).
% 0.56/0.32 thf(func_def_210, type, sK123: ((real > real) > real)).
% 0.56/0.32 thf(func_def_211, type, sK124: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_212, type, sK125: ((real > nat) > real)).
% 0.56/0.32 thf(func_def_213, type, sK126: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_214, type, sK127: ((nat > real) > nat)).
% 0.56/0.32 thf(func_def_215, type, sK128: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_216, type, sK129: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_217, type, sK130: ((product_prod_a_real > $o) > a)).
% 0.56/0.32 thf(func_def_218, type, sK131: ((product_prod_a_real > $o) > real)).
% 0.56/0.32 thf(func_def_219, type, sK132: ((produc1691597095_set_a > $o) > set_a)).
% 0.56/0.32 thf(func_def_220, type, sK133: ((produc1691597095_set_a > $o) > set_a)).
% 0.56/0.32 thf(func_def_221, type, sK134: (product_prod_a_real > a)).
% 0.56/0.32 thf(func_def_222, type, sK135: (product_prod_a_real > real)).
% 0.56/0.32 thf(func_def_223, type, sK136: (produc1691597095_set_a > set_a)).
% 0.56/0.32 thf(func_def_224, type, sK137: (produc1691597095_set_a > set_a)).
% 0.56/0.32 thf(func_def_225, type, sK138: ((product_prod_a_real > $o) > a)).
% 0.56/0.32 thf(func_def_226, type, sK139: ((product_prod_a_real > $o) > real)).
% 0.56/0.32 thf(func_def_227, type, sK140: ((produc1691597095_set_a > $o) > set_a)).
% 0.56/0.32 thf(func_def_228, type, sK141: ((produc1691597095_set_a > $o) > set_a)).
% 0.56/0.32 thf(func_def_229, type, sK142: (product_prod_a_real > a)).
% 0.56/0.32 thf(func_def_230, type, sK143: (product_prod_a_real > real)).
% 0.56/0.32 thf(func_def_231, type, sK144: (produc1691597095_set_a > set_a)).
% 0.56/0.32 thf(func_def_232, type, sK145: (produc1691597095_set_a > set_a)).
% 0.56/0.32 thf(func_def_233, type, sK146: a).
% 0.56/0.32 thf(func_def_234, type, sK147: real).
% 0.56/0.32 thf(func_def_235, type, sK148: product_prod_a_real).
% 0.56/0.32 thf(func_def_236, type, sK149: (set_a > a)).
% 0.56/0.32 thf(func_def_237, type, sK150: (set_real > real)).
% 0.56/0.32 thf(func_def_238, type, sK151: (set_Pr1928503567a_real > product_prod_a_real)).
% 0.56/0.32 thf(func_def_239, type, sK152: ((nat > real) > nat > nat)).
% 0.56/0.32 thf(func_def_240, type, sK153: ((nat > real) > (nat > real) > nat > nat)).
% 0.56/0.32 thf(func_def_241, type, sK154: ((nat > $o) > nat)).
% 0.56/0.32 thf(func_def_242, type, sK155: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_243, type, sK156: ((nat > nat) > nat)).
% 0.56/0.32 thf(func_def_244, type, sK157: ((nat > $o) > nat)).
% 0.56/0.32 thf(func_def_245, type, sK158: (nat > (nat > $o) > nat)).
% 0.56/0.32 thf(func_def_246, type, sK159: (nat > (nat > $o) > nat)).
% 0.56/0.32 thf(func_def_247, type, sK160: ((nat > $o) > nat)).
% 0.56/0.32 thf(func_def_248, type, sK161: ((nat > $o) > nat)).
% 0.56/0.32 thf(func_def_249, type, sK162: ((nat > $o) > nat > nat)).
% 0.56/0.32 thf(func_def_250, type, sK163: ((nat > $o) > nat > nat)).
% 0.56/0.32 thf(func_def_251, type, sK164: (set_real > real)).
% 0.56/0.32 thf(func_def_252, type, sK165: (real > set_real > real)).
% 0.56/0.32 thf(func_def_253, type, sK166: (real > set_real > real)).
% 0.56/0.32 thf(func_def_254, type, sK167: (set_Pr1928503567a_real > product_prod_a_real > real > product_prod_a_real)).
% 0.56/0.32 thf(func_def_255, type, sK168: (set_Pr1928503567a_real > product_prod_a_real > real)).
% 0.56/0.32 thf(func_def_256, type, sK169: (set_a > a > real > a)).
% 0.56/0.32 thf(func_def_257, type, sK170: (set_a > a > real)).
% 0.56/0.32 thf(func_def_258, type, sK171: (set_real > real > real > real)).
% 0.56/0.32 thf(func_def_259, type, sK172: (set_real > real > real)).
% 0.56/0.32 thf(func_def_260, type, sK173: (set_Pr1928503567a_real > product_prod_a_real > product_prod_a_real > product_prod_a_real)).
% 0.56/0.32 thf(func_def_261, type, sK174: (set_a > a > a > a)).
% 0.56/0.32 thf(func_def_262, type, sK175: (set_real > real > real > real)).
% 0.56/0.32 thf(f1,axiom,(
% 0.56/0.32 ? [X0 : product_prod_a_real] : ((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f)))),
% 0.56/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062_092_060exists_062ya_092_060in_062Epigraph_AUNIV_Af_O_Adist_Aya_A_Ix_M_Ay_J_A_060_Ae_092_060close_062)).
% 0.56/0.32 thf(f281,axiom,(
% 0.56/0.32 ! [X0 : product_prod_a_real] : ~ ! [X1 : a,X2 : real] : (X0 != ((product_Pair_a_real @ X1 @ X2)))),
% 0.56/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_old_Oprod_Oexhaust)).
% 0.56/0.32 thf(f345,axiom,(
% 0.56/0.32 ! [X0 : a,X1 : real] : (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) => thesis)),
% 0.56/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.56/0.32 thf(f346,conjecture,(
% 0.56/0.32 thesis),
% 0.56/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.56/0.32 thf(f347,negated_conjecture,(
% 0.56/0.32 ~thesis),
% 0.56/0.32 inference(negated_conjecture,[status(cth)],[f346])).
% 0.56/0.32 thf(f348,plain,(
% 0.56/0.32 ? [X0 : product_prod_a_real] : ((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f)))),
% 0.56/0.32 inference(rectify,[],[f1])).
% 0.56/0.32 thf(f349,plain,(
% 0.56/0.32 ? [X0 : product_prod_a_real] : ((((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e)) = $true) & (((member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f))) = $true))),
% 0.56/0.32 inference(fool_elimination,[],[f348])).
% 0.56/0.32 thf(f963,plain,(
% 0.56/0.32 ! [X0 : a,X1 : real] : (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e) & (member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) => thesis)),
% 0.56/0.32 inference(rectify,[],[f345])).
% 0.56/0.32 thf(f964,plain,(
% 0.56/0.32 ! [X0 : a,X1 : real] : (((((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) = $true) & (((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) = $true)) => (thesis = $true))),
% 0.56/0.32 inference(fool_elimination,[],[f963])).
% 0.56/0.32 thf(f965,plain,(
% 0.56/0.32 ~thesis),
% 0.56/0.32 inference(rectify,[],[f347])).
% 0.56/0.32 thf(f966,plain,(
% 0.56/0.32 ~ (thesis = $true)),
% 0.56/0.32 inference(fool_elimination,[],[f965])).
% 0.56/0.32 thf(f1016,plain,(
% 0.56/0.32 (thesis != $true)),
% 0.56/0.32 inference(flattening,[],[f966])).
% 0.56/0.32 thf(f1309,plain,(
% 0.56/0.32 ! [X0 : product_prod_a_real] : ? [X1 : a,X2 : real] : (((product_Pair_a_real @ X1 @ X2)) = X0)),
% 0.56/0.32 inference(ennf_transformation,[],[f281])).
% 0.56/0.32 thf(f1350,plain,(
% 0.56/0.32 ! [X0 : a,X1 : real] : ((thesis = $true) | ((((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true)))),
% 0.56/0.32 inference(ennf_transformation,[],[f964])).
% 0.56/0.32 thf(f1351,plain,(
% 0.56/0.32 ! [X0 : a,X1 : real] : ((thesis = $true) | (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true))),
% 0.56/0.32 inference(flattening,[],[f1350])).
% 0.56/0.32 thf(f1360,plain,(
% 0.56/0.32 ($true = ((ord_less_real @ (real_V404783528a_real @ sK6 @ (product_Pair_a_real @ x @ y)) @ e))) & ($true = ((member1103263856a_real @ sK6 @ (lower_930854854raph_a @ top_top_set_a @ f))))),
% 0.56/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f349])).
% 0.56/0.32 thf(f1440,plain,(
% 0.56/0.32 ! [X0 : product_prod_a_real] : (((product_Pair_a_real @ (sK134 @ X0) @ (sK135 @ X0))) = X0)),
% 0.56/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK8 @ X1),skolemize(X5,sK8 @ X1)],[f1309])).
% 0.56/0.32 thf(f1465,plain,(
% 0.56/0.32 ($true = ((member1103263856a_real @ sK6 @ (lower_930854854raph_a @ top_top_set_a @ f))))),
% 0.56/0.32 inference(cnf_transformation,[],[f1360])).
% 0.56/0.32 thf(f1466,plain,(
% 0.56/0.32 ($true = ((ord_less_real @ (real_V404783528a_real @ sK6 @ (product_Pair_a_real @ x @ y)) @ e)))),
% 0.56/0.32 inference(cnf_transformation,[],[f1360])).
% 0.56/0.32 thf(f1841,plain,(
% 0.56/0.32 ( ! [X0 : product_prod_a_real] : ((((product_Pair_a_real @ (sK134 @ X0) @ (sK135 @ X0))) = X0)) )),
% 0.56/0.32 inference(cnf_transformation,[],[f1440])).
% 0.56/0.32 thf(f1931,plain,(
% 0.56/0.32 ( ! [X0 : a,X1 : real] : ((thesis = $true) | (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true)) )),
% 0.56/0.32 inference(cnf_transformation,[],[f1351])).
% 0.56/0.32 thf(f1932,plain,(
% 0.56/0.32 (thesis != $true)),
% 0.56/0.32 inference(cnf_transformation,[],[f1016])).
% 0.56/0.32 thf(f1934,definition,(
% 0.56/0.32 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.56/0.32 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.56/0.32 thf(f4215,plain,(
% 0.56/0.32 ( ! [X0 : a,X1 : real] : ((((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) != $true) | (((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true)) )),
% 0.56/0.32 inference(forward_subsumption_resolution,[],[f1931,f1932])).
% 0.56/0.32 thf(f4254,plain,(
% 0.56/0.32 ( ! [X0 : a,X1 : real] : (($true != $true) | (((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true) | (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) = $false)) )),
% 0.56/0.32 inference(constrained_superposition,[],[f4215,f1934])).
% 0.56/0.32 thf(f4255,plain,(
% 0.56/0.32 ( ! [X0 : a,X1 : real] : ((((member1103263856a_real @ (product_Pair_a_real @ X0 @ X1) @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true) | (((ord_less_real @ (real_V404783528a_real @ (product_Pair_a_real @ X0 @ X1) @ (product_Pair_a_real @ x @ y)) @ e)) = $false)) )),
% 0.56/0.32 inference(trivial_inequality_removal,[],[f4254])).
% 0.56/0.32 thf(f4616,plain,(
% 0.56/0.32 ( ! [X0 : product_prod_a_real] : ((((member1103263856a_real @ X0 @ (lower_930854854raph_a @ top_top_set_a @ f))) != $true) | (((ord_less_real @ (real_V404783528a_real @ X0 @ (product_Pair_a_real @ x @ y)) @ e)) = $false)) )),
% 0.56/0.32 inference(constrained_superposition,[],[f4255,f1841])).
% 0.56/0.32 thf(f4754,plain,(
% 0.56/0.32 ($true != $true) | (((ord_less_real @ (real_V404783528a_real @ sK6 @ (product_Pair_a_real @ x @ y)) @ e)) = $false)),
% 0.56/0.32 inference(constrained_superposition,[],[f4616,f1465])).
% 0.56/0.32 thf(f4764,plain,(
% 0.56/0.32 (((ord_less_real @ (real_V404783528a_real @ sK6 @ (product_Pair_a_real @ x @ y)) @ e)) = $false)),
% 0.56/0.32 inference(trivial_inequality_removal,[],[f4754])).
% 0.56/0.32 thf(f5007,plain,(
% 0.56/0.32 ($true = $false)),
% 0.56/0.32 inference(constrained_superposition,[],[f4764,f1466])).
% 0.56/0.32 thf(f5020,plain,(
% 0.56/0.32 $false),
% 0.56/0.32 inference(trivial_inequality_removal,[],[f5007])).
% 0.56/0.32 % SZS output end Proof for theBenchmark
% 0.56/0.32 % (605921)------------------------------
% 0.56/0.32 % (605921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.56/0.32 % (605921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.32 % (605921)CaDiCaL version: 2.1.3
% 0.56/0.32 % (605921)Termination reason: Refutation
% 0.56/0.32 % (605921)Time elapsed: 0.079 s
% 0.56/0.32 % (605921)Peak memory usage: 15 MB
% 0.56/0.32 % (605921)Instructions burned: 320 (million)
% 0.56/0.32 % (605891)Success in time 0.189 s
% 0.56/0.32 % Vampire exiting
%------------------------------------------------------------------------------