%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP162^2 : 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 : n002.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 08:10:56 AM UTC 2026
% Result : Theorem 1.85s 0.53s
% Output : Refutation 1.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP162^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 20:06:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 1.85/0.53 % (1785325)Will run a generic schedule for satisfiability detection.
% 1.85/0.53 % (1785331)% WARNING: option uhcvi not known.
% 1.85/0.53 % (1785331)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1381150387:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.85/0.53 % (1785330)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=868734264_2999 on theBenchmark for (2999ds/0Mi)
% 1.85/0.53 % (1785332)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4162718569:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.85/0.53 % (1785331)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % (1785333)dis+10_1_sil=32000:sp=arity:random_seed=1217901125:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.85/0.53 % (1785334)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=774494226:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.85/0.53 % (1785336)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4161576548:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.85/0.53 % (1785331)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.85/0.53 % (1785335)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4236717131:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.85/0.53 % (1785334)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (1785333)Instruction limit reached!
% 1.85/0.53 % (1785333)------------------------------
% 1.85/0.53 % (1785333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (1785333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (1785333)CaDiCaL version: 2.1.3
% 1.85/0.53 % (1785333)Termination reason: Instruction limit
% 1.85/0.53 % (1785333)Termination phase: Saturation
% 1.85/0.53 % (1785333)Time elapsed: 0.046 s
% 1.85/0.53 % (1785333)Peak memory usage: 13 MB
% 1.85/0.53 % (1785333)Instructions burned: 104 (million)
% 1.85/0.53 % (1785334)Instruction limit reached!
% 1.85/0.53 % (1785334)------------------------------
% 1.85/0.53 % (1785334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (1785334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (1785334)CaDiCaL version: 2.1.3
% 1.85/0.53 % (1785334)Termination reason: Instruction limit
% 1.85/0.53 % (1785334)Termination phase: Saturation
% 1.85/0.53 % (1785334)Time elapsed: 0.052 s
% 1.85/0.53 % (1785334)Peak memory usage: 13 MB
% 1.85/0.53 % (1785334)Instructions burned: 116 (million)
% 1.85/0.53 % (1785344)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3107943249:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.85/0.53 % (1785345)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3724324308:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.85/0.53 % (1785347)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=3542587517:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.85/0.53 % (1785336)Instruction limit reached!
% 1.85/0.53 % (1785336)------------------------------
% 1.85/0.53 % (1785336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (1785336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (1785336)CaDiCaL version: 2.1.3
% 1.85/0.53 % (1785336)Termination reason: Instruction limit
% 1.85/0.53 % (1785336)Termination phase: Saturation
% 1.85/0.53 % (1785336)Time elapsed: 0.076 s
% 1.85/0.53 % (1785336)Peak memory usage: 14 MB
% 1.85/0.53 % (1785336)Instructions burned: 159 (million)
% 1.85/0.53 % (1785335)Instruction limit reached!
% 1.85/0.53 % (1785335)------------------------------
% 1.85/0.53 % (1785335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (1785335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (1785335)CaDiCaL version: 2.1.3
% 1.85/0.53 % (1785335)Termination reason: Instruction limit
% 1.85/0.53 % (1785335)Termination phase: Saturation
% 1.85/0.53 % (1785335)Time elapsed: 0.066 s
% 1.85/0.53 % (1785335)Peak memory usage: 13 MB
% 1.85/0.53 % (1785335)Instructions burned: 132 (million)
% 1.85/0.53 % (1785347)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (1785350)ott-21_1_sil=16000:fs=off:random_seed=4026725653:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.85/0.53 % (1785351)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=446968929:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.85/0.53 % (1785352)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2616112950:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.85/0.53 % (1785347)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.85/0.53 % (1785345)Instruction limit reached!
% 1.85/0.53 % (1785345)------------------------------
% 1.85/0.53 % (1785345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (1785345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (1785345)CaDiCaL version: 2.1.3
% 1.85/0.53 % (1785345)Termination reason: Instruction limit
% 1.85/0.53 % (1785345)Termination phase: Saturation
% 1.85/0.53 % (1785345)Time elapsed: 0.064 s
% 1.85/0.53 % (1785345)Peak memory usage: 13 MB
% 1.85/0.53 % (1785345)Instructions burned: 133 (million)
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (1785356)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2629296277:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.85/0.53 % (1785357)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1812243808:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.85/0.53 % (1785350)Instruction limit reached!
% 1.85/0.53 % (1785350)------------------------------
% 1.85/0.53 % (1785350)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (1785350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (1785350)CaDiCaL version: 2.1.3
% 1.85/0.53 % (1785350)Termination reason: Instruction limit
% 1.85/0.53 % (1785350)Termination phase: Saturation
% 1.85/0.53 % (1785350)Time elapsed: 0.088 s
% 1.85/0.53 % (1785350)Peak memory usage: 13 MB
% 1.85/0.53 % (1785350)Instructions burned: 188 (million)
% 1.85/0.53 % Exception at run slice level
% 1.85/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.85/0.53 % (1785360)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=263161076: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)
% 1.85/0.53 % (1785361)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=1249320498:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 1.85/0.53 % (1785360)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % (1785361)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.85/0.53 % (1785331) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1785325-1785331"...
% 1.85/0.53 % (1785331)...printing done.
% 1.85/0.53 % (1785331)Refutation found. Thanks to Tanya!
% 1.85/0.53 % SZS status Theorem for theBenchmark
% 1.85/0.53 % SZS output start Proof for theBenchmark
% 1.85/0.53 thf(type_def_5, type, refine1665802226e_nres: $tType > $tType).
% 1.85/0.53 thf(type_def_6, type, product_unit: $tType).
% 1.85/0.53 thf(type_def_7, type, set: $tType > $tType).
% 1.85/0.53 thf(type_def_8, type, a: $tType).
% 1.85/0.53 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 1.85/0.53 thf(func_def_0, type, bounded_lattice: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_1, type, type: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_4, type, top: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_6, type, lattice: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_7, type, linorder: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_8, type, preorder: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_9, type, order_bot: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_10, type, semilattice_inf: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_11, type, bounded_lattice_bot: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_12, type, bounde1561333602nf_top: !>[X0: $tType]:($o)).
% 1.85/0.53 thf(func_def_13, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 1.85/0.53 thf(func_def_14, type, inf_inf: !>[X0: $tType]:((X0 > X0 > X0))).
% 1.85/0.53 thf(func_def_15, type, bot_bot: !>[X0: $tType]:(X0)).
% 1.85/0.53 thf(func_def_16, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.85/0.53 thf(func_def_17, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_18, type, top_top: !>[X0: $tType]:(X0)).
% 1.85/0.53 thf(func_def_19, type, refine1687780735RETURN: !>[X0: $tType]:((X0 > refine1665802226e_nres @ X0))).
% 1.85/0.53 thf(func_def_20, type, refine463715084e_bind: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X0 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X1))).
% 1.85/0.53 thf(func_def_21, type, refine1315500908_inres: !>[X0: $tType]:((refine1665802226e_nres @ X0 > X0 > $o))).
% 1.85/0.53 thf(func_def_22, type, refine406925620_inres: !>[X0: $tType]:((refine1665802226e_nres @ X0 > X0 > $o))).
% 1.85/0.53 thf(func_def_23, type, refine1102455758nofail: !>[X0: $tType]:((refine1665802226e_nres @ X0 > $o))).
% 1.85/0.53 thf(func_def_24, type, refine1767639642_FAILi: !>[X0: $tType]:(refine1665802226e_nres @ X0)).
% 1.85/0.53 thf(func_def_25, type, refine605929679le_RES: !>[X0: $tType]:((set @ X0 > refine1665802226e_nres @ X0))).
% 1.85/0.53 thf(func_def_26, type, refine1442219249c_nres: !>[X0: $tType, X1: $tType]:((X0 > (set @ X1 > X0) > refine1665802226e_nres @ X1 > X0))).
% 1.85/0.53 thf(func_def_27, type, refine1672542526he_RES: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_28, type, powp: !>[X0: $tType]:(((X0 > $o) > set @ X0 > $o))).
% 1.85/0.53 thf(func_def_29, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_30, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 1.85/0.53 thf(func_def_31, type, a2: refine1665802226e_nres @ a).
% 1.85/0.53 thf(func_def_32, type, p: (a > $o)).
% 1.85/0.53 thf(func_def_33, type, q: (a > $o)).
% 1.85/0.53 thf(func_def_35, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.85/0.53 thf(func_def_38, type, vIMP: ($o > $o > $o)).
% 1.85/0.53 thf(func_def_39, type, db0: !>[X0: $tType]:(X0)).
% 1.85/0.53 thf(func_def_40, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.85/0.53 thf(func_def_41, type, vNOT: ($o > $o)).
% 1.85/0.53 thf(func_def_42, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.85/0.53 thf(func_def_43, type, db2: !>[X0: $tType]:(X0)).
% 1.85/0.53 thf(func_def_44, type, db1: !>[X0: $tType]:(X0)).
% 1.85/0.53 thf(func_def_45, type, vAND: ($o > $o > $o)).
% 1.85/0.53 thf(func_def_46, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.85/0.53 thf(func_def_47, type, vOR: ($o > $o > $o)).
% 1.85/0.53 thf(func_def_48, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 1.85/0.53 thf(func_def_49, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 1.85/0.53 thf(func_def_50, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 1.85/0.53 thf(func_def_51, type, sP3: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o))).
% 1.85/0.53 thf(func_def_52, type, sP4: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o > $o))).
% 1.85/0.53 thf(func_def_53, type, sK5: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 1.85/0.53 thf(func_def_54, type, sK6: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_55, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_56, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.85/0.53 thf(func_def_57, type, sK9: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.85/0.53 thf(func_def_58, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.85/0.53 thf(func_def_59, type, sK11: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 1.85/0.53 thf(func_def_60, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.85/0.53 thf(func_def_61, type, sK13: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_62, type, sK14: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_63, type, sK15: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_64, type, sK16: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_65, type, sK17: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_66, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 1.85/0.53 thf(func_def_67, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.85/0.53 thf(func_def_68, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.85/0.53 thf(func_def_69, type, sK21: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.85/0.53 thf(func_def_70, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 1.85/0.53 thf(func_def_71, type, sK23: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.85/0.53 thf(func_def_72, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 1.85/0.53 thf(func_def_73, type, sK25: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.85/0.53 thf(func_def_74, type, sK26: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.85/0.53 thf(func_def_75, type, sK27: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.85/0.53 thf(func_def_76, type, sK28: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.85/0.53 thf(func_def_77, type, sK29: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.85/0.53 thf(func_def_78, type, sK30: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.85/0.53 thf(func_def_79, type, sK31: !>[X0: $tType]:(((X0 > X0 > X0) > X0))).
% 1.85/0.53 thf(func_def_80, type, sK32: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 1.85/0.53 thf(func_def_81, type, sK33: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_82, type, sK34: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 1.85/0.53 thf(func_def_83, type, sK35: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_84, type, sK36: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 1.85/0.53 thf(func_def_85, type, sK37: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_86, type, sK38: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_87, type, sK39: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_88, type, sK40: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_89, type, sK41: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_90, type, sK42: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_91, type, sK43: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_92, type, sK44: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_93, type, sK45: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_94, type, sK46: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_95, type, sK47: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > refine1665802226e_nres @ X0))).
% 1.85/0.53 thf(func_def_96, type, sK48: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_97, type, sK49: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_98, type, sK50: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_99, type, sK51: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > refine1665802226e_nres @ X0))).
% 1.85/0.53 thf(func_def_100, type, sK52: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_101, type, sK53: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_102, type, sK54: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > set @ X0))).
% 1.85/0.53 thf(func_def_103, type, sK55: !>[X0: $tType]:(((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o) > refine1665802226e_nres @ X0))).
% 1.85/0.53 thf(func_def_104, type, sK56: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o > set @ X0))).
% 1.85/0.53 thf(func_def_105, type, sK57: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > $o > set @ X0))).
% 1.85/0.53 thf(func_def_106, type, sK58: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_107, type, sK59: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_108, type, sK60: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_109, type, sK61: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_110, type, sK62: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_111, type, sK63: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_112, type, sK64: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_113, type, sK65: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0 > X0))).
% 1.85/0.53 thf(func_def_114, type, sK66: !>[X0: $tType]:((refine1665802226e_nres @ X0 > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_115, type, sK67: !>[X0: $tType, X1: $tType]:(((X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X0 > refine1665802226e_nres @ X1 > X0))).
% 1.85/0.53 thf(func_def_116, type, sK68: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1))).
% 1.85/0.53 thf(func_def_117, type, sK69: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1))).
% 1.85/0.53 thf(func_def_118, type, sK70: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > (X0 > refine1665802226e_nres @ X1) > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_119, type, sK71: !>[X0: $tType, X1: $tType]:((refine1665802226e_nres @ X1 > (X0 > refine1665802226e_nres @ X1) > refine1665802226e_nres @ X0 > X0))).
% 1.85/0.53 thf(func_def_120, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > $o) > (X1 > refine1665802226e_nres @ X2) > (X0 > $o) > (X1 > refine1665802226e_nres @ X0) > refine1665802226e_nres @ X1 > X1))).
% 1.85/0.53 thf(func_def_121, type, sK73: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_122, type, sK74: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > X1 > set @ X0))).
% 1.85/0.53 thf(func_def_123, type, sK75: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > refine1665802226e_nres @ X0) > X1))).
% 1.85/0.53 thf(func_def_124, type, sK76: !>[X0: $tType, X1: $tType]:(((X1 > refine1665802226e_nres @ X0) > set @ X1 > set @ X0))).
% 1.85/0.53 thf(func_def_125, type, sK77: !>[X0: $tType]:(set @ X0)).
% 1.85/0.53 thf(func_def_126, type, sK78: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_127, type, sK79: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_128, type, sK80: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_129, type, sK81: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_130, type, sK82: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_131, type, sK83: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_132, type, sK84: !>[X0: $tType]:((refine1665802226e_nres @ X0 > refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_133, type, sK85: !>[X0: $tType, X1: $tType]:((X1 > (X1 > refine1665802226e_nres @ X0) > set @ X0))).
% 1.85/0.53 thf(func_def_134, type, sK86: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_135, type, sK87: !>[X0: $tType]:((refine1665802226e_nres @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_136, type, sK88: !>[X0: $tType]:((X0 > set @ X0))).
% 1.85/0.53 thf(func_def_137, type, sK89: !>[X0: $tType]:((set @ X0 > set @ X0))).
% 1.85/0.53 thf(func_def_138, type, sK90: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_139, type, sK91: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 1.85/0.53 thf(func_def_140, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 1.85/0.53 thf(f5,axiom,(
% 1.85/0.53 (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q))))),
% 1.85/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062A_A_092_060le_062_Ainf_A_ISPEC_AP_J_A_ISPEC_AQ_J_092_060close_062)).
% 1.85/0.53 thf(f66,axiom,(
% 1.85/0.53 ! [X0 : $tType,X1 : set @ X0,X2 : set @ X0] : (((inf_inf @ refine1665802226e_nres @ X0 @ (refine605929679le_RES @ X0 @ X1) @ (refine605929679le_RES @ X0 @ X2))) = ((refine605929679le_RES @ X0 @ (inf_inf @ set @ X0 @ X1 @ X2))))),
% 1.85/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_inf__nres_Osimps_I3_J)).
% 1.85/0.53 thf(f127,axiom,(
% 1.85/0.53 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((collect @ X0 @ (^[X3 : X0] : ((X2 @ X3) & (X1 @ X3))))) = ((inf_inf @ set @ X0 @ (collect @ X0 @ X1) @ (collect @ X0 @ X2))))),
% 1.85/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_Collect__conj__eq)).
% 1.85/0.53 thf(f309,axiom,(
% 1.85/0.53 ! [X0 : $o] : ((X0 = $false) | (X0 = $true))),
% 1.85/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T)).
% 1.85/0.53 thf(f312,conjecture,(
% 1.85/0.53 (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[X0 : a] : ((q @ X0) & (p @ X0))))))),
% 1.85/0.53 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 1.85/0.53 thf(f313,negated_conjecture,(
% 1.85/0.53 ~(ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[X0 : a] : ((q @ X0) & (p @ X0))))))),
% 1.85/0.53 inference(negated_conjecture,[status(cth)],[f312])).
% 1.85/0.53 thf(f321,plain,(
% 1.85/0.53 (ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q))))),
% 1.85/0.53 inference(rectify,[],[f5])).
% 1.85/0.53 thf(f322,plain,(
% 1.85/0.53 (((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q))))) = $true)),
% 1.85/0.53 inference(fool_elimination,[],[f321])).
% 1.85/0.53 thf(f540,plain,(
% 1.85/0.53 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((collect @ X0 @ (^[X3 : X0] : ((X2 @ X3) & (X1 @ X3))))) = ((inf_inf @ set @ X0 @ (collect @ X0 @ X1) @ (collect @ X0 @ X2))))),
% 1.85/0.53 inference(rectify,[],[f127])).
% 1.85/0.53 thf(f541,plain,(
% 1.85/0.53 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((inf_inf @ set @ X0 @ (collect @ X0 @ X1) @ (collect @ X0 @ X2))) = ((collect @ X0 @ (^[Y0 : X0]: ((X1 @ Y0) & (X2 @ Y0))))))),
% 1.85/0.53 inference(fool_elimination,[],[f540])).
% 1.85/0.53 thf(f865,plain,(
% 1.85/0.53 ! [X0 : $o] : (($false = X0) | ($true = X0))),
% 1.85/0.53 inference(fool_elimination,[],[f309])).
% 1.85/0.53 thf(f870,plain,(
% 1.85/0.53 ~(ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[X0 : a] : ((q @ X0) & (p @ X0))))))),
% 1.85/0.53 inference(rectify,[],[f313])).
% 1.85/0.53 thf(f871,plain,(
% 1.85/0.53 ~ ($true = ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0))))))))),
% 1.85/0.53 inference(fool_elimination,[],[f870])).
% 1.85/0.53 thf(f890,plain,(
% 1.85/0.53 ($true != ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0))))))))),
% 1.85/0.53 inference(flattening,[],[f871])).
% 1.85/0.53 thf(f1208,plain,(
% 1.85/0.53 (((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (inf_inf @ refine1665802226e_nres @ a @ (refine605929679le_RES @ a @ (collect @ a @ p)) @ (refine605929679le_RES @ a @ (collect @ a @ q))))) = $true)),
% 1.85/0.53 inference(cnf_transformation,[],[f322])).
% 1.85/0.53 thf(f1303,plain,(
% 1.85/0.53 ( ! [X0 : $tType,X2 : set @ X0,X1 : set @ X0] : ((((inf_inf @ refine1665802226e_nres @ X0 @ (refine605929679le_RES @ X0 @ X1) @ (refine605929679le_RES @ X0 @ X2))) = ((refine605929679le_RES @ X0 @ (inf_inf @ set @ X0 @ X1 @ X2))))) )),
% 1.85/0.53 inference(cnf_transformation,[],[f66])).
% 1.85/0.53 thf(f1371,plain,(
% 1.85/0.53 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : ((((inf_inf @ set @ X0 @ (collect @ X0 @ X1) @ (collect @ X0 @ X2))) = ((collect @ X0 @ (^[Y0 : X0]: ((X1 @ Y0) & (X2 @ Y0))))))) )),
% 1.85/0.53 inference(cnf_transformation,[],[f541])).
% 1.85/0.53 thf(f1605,plain,(
% 1.85/0.53 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.85/0.53 inference(cnf_transformation,[],[f865])).
% 1.85/0.53 thf(f1608,plain,(
% 1.85/0.53 ($true != ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0))))))))),
% 1.85/0.53 inference(cnf_transformation,[],[f890])).
% 1.85/0.53 thf(f2010,plain,(
% 1.85/0.53 ($true != $true) | ($false = ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0))))))))),
% 1.85/0.53 inference(constrained_superposition,[],[f1608,f1605])).
% 1.85/0.53 thf(f2012,plain,(
% 1.85/0.53 ($false = ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0))))))))),
% 1.85/0.53 inference(trivial_inequality_removal,[],[f2010])).
% 1.85/0.53 thf(f10488,plain,(
% 1.85/0.53 ($true = ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (inf_inf @ set @ a @ (collect @ a @ p) @ (collect @ a @ q))))))),
% 1.85/0.53 inference(forward_demodulation,[],[f1208,f1303])).
% 1.85/0.53 thf(f10760,plain,(
% 1.85/0.53 ($true = ((ord_less_eq @ refine1665802226e_nres @ a @ a2 @ (refine605929679le_RES @ a @ (collect @ a @ (^[Y0 : a]: ((p @ Y0) & (q @ Y0))))))))),
% 1.85/0.53 inference(constrained_superposition,[],[f10488,f1371])).
% 1.85/0.53 thf(f10779,plain,(
% 1.85/0.53 ($true = $false)),
% 1.85/0.53 inference(forward_demodulation,[],[f10760,f2012])).
% 1.85/0.53 thf(f10780,plain,(
% 1.85/0.53 $false),
% 1.85/0.53 inference(trivial_inequality_removal,[],[f10779])).
% 1.85/0.53 % SZS output end Proof for theBenchmark
% 1.85/0.53 % (1785331)------------------------------
% 1.85/0.53 % (1785331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.85/0.53 % (1785331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.85/0.53 % (1785331)CaDiCaL version: 2.1.3
% 1.85/0.53 % (1785331)Termination reason: Refutation
% 1.85/0.53 % (1785331)Time elapsed: 0.261 s
% 1.85/0.53 % (1785331)Peak memory usage: 18 MB
% 1.85/0.53 % (1785331)Instructions burned: 978 (million)
% 1.85/0.53 % (1785325)Success in time 0.308 s
% 1.85/0.53 % Vampire exiting
%------------------------------------------------------------------------------