%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM195^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 07:46:31 AM UTC 2026
% Result : Theorem 0.78s 0.37s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM195^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:48:56 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.78/0.37 % (3711073)Will run a generic schedule for satisfiability detection.
% 0.78/0.37 % (3711083)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=564595209:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.78/0.37 % (3711079)% WARNING: option uhcvi not known.
% 0.78/0.37 % (3711079)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=228322048:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.78/0.37 % (3711078)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2248996355_2999 on theBenchmark for (2999ds/0Mi)
% 0.78/0.37 % (3711080)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4143037376:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.78/0.37 % (3711081)dis+10_1_sil=32000:sp=arity:random_seed=3233187198:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.78/0.37 % (3711082)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=715438719:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.78/0.37 % (3711084)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2459553299:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.78/0.37 % (3711079)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.78/0.37 % (3711082)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.78/0.37 % (3711083)Instruction limit reached!
% 0.78/0.37 % (3711083)------------------------------
% 0.78/0.37 % (3711083)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.37 % (3711083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.37 % (3711083)CaDiCaL version: 2.1.3
% 0.78/0.37 % (3711083)Termination reason: Instruction limit
% 0.78/0.37 % (3711083)Termination phase: Saturation
% 0.78/0.37 % (3711083)Time elapsed: 0.029 s
% 0.78/0.37 % (3711083)Peak memory usage: 13 MB
% 0.78/0.37 % (3711083)Instructions burned: 131 (million)
% 0.78/0.37 % (3711092)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3323343209:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.78/0.37 % Exception at run slice level
% 0.78/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.78/0.37 % (3711079)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.78/0.37 % (3711081)Instruction limit reached!
% 0.78/0.37 % (3711081)------------------------------
% 0.78/0.37 % (3711081)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.37 % (3711081)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.37 % (3711081)CaDiCaL version: 2.1.3
% 0.78/0.37 % (3711081)Termination reason: Instruction limit
% 0.78/0.37 % (3711081)Termination phase: Saturation
% 0.78/0.37 % (3711081)Time elapsed: 0.044 s
% 0.78/0.37 % (3711081)Peak memory usage: 12 MB
% 0.78/0.37 % (3711081)Instructions burned: 104 (million)
% 0.78/0.37 % (3711082)Instruction limit reached!
% 0.78/0.37 % (3711082)------------------------------
% 0.78/0.37 % (3711082)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.37 % (3711082)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.37 % (3711082)CaDiCaL version: 2.1.3
% 0.78/0.37 % (3711082)Termination reason: Instruction limit
% 0.78/0.37 % (3711082)Termination phase: Saturation
% 0.78/0.37 % (3711082)Time elapsed: 0.049 s
% 0.78/0.37 % (3711082)Peak memory usage: 13 MB
% 0.78/0.37 % (3711082)Instructions burned: 116 (million)
% 0.78/0.37 % Exception at run slice level
% 0.78/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.78/0.37 % (3711096)ott-21_1_sil=16000:fs=off:random_seed=18060067:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.78/0.37 % (3711094)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3313541419:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.78/0.37 % (3711095)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=4097894742:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.78/0.37 % (3711084)Instruction limit reached!
% 0.78/0.37 % (3711084)------------------------------
% 0.78/0.37 % (3711084)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.37 % (3711084)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.37 % (3711084)CaDiCaL version: 2.1.3
% 0.78/0.37 % (3711084)Termination reason: Instruction limit
% 0.78/0.37 % (3711084)Termination phase: Saturation
% 0.78/0.37 % (3711084)Time elapsed: 0.068 s
% 0.78/0.37 % (3711084)Peak memory usage: 13 MB
% 0.78/0.37 % (3711084)Instructions burned: 160 (million)
% 0.78/0.37 % (3711097)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2133747414:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.78/0.37 % (3711080) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3711073-3711080"...
% 0.78/0.37 % (3711080)...printing done.
% 0.78/0.37 % (3711080)Refutation found. Thanks to Tanya!
% 0.78/0.37 % SZS status Theorem for theBenchmark
% 0.78/0.37 % SZS output start Proof for theBenchmark
% 0.78/0.37 thf(type_def_5, type, set: $tType > $tType).
% 0.78/0.37 thf(type_def_6, type, itself: $tType > $tType).
% 0.78/0.37 thf(type_def_7, type, a: $tType).
% 0.78/0.37 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 0.78/0.37 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_1, type, uminus: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_2, type, ord: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_3, type, order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_4, type, group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_5, type, no_bot: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_6, type, no_top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_7, type, linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_8, type, preorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_9, type, wellorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_10, type, dense_order: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_11, type, boolean_algebra: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_12, type, semilattice_sup: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_13, type, dense_linorder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_15, type, condit1656338222tinuum: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_16, type, condit1037483654norder: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.78/0.37 thf(func_def_17, type, gram_L1456083582e_leqv: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > $o))).
% 0.78/0.37 thf(func_def_18, type, gram_L608943123e_subs: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > $o))).
% 0.78/0.37 thf(func_def_19, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_20, type, sup_sup: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.78/0.37 thf(func_def_21, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.78/0.37 thf(func_def_22, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.78/0.37 thf(func_def_23, type, order_antimono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.78/0.37 thf(func_def_24, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.78/0.37 thf(func_def_25, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.78/0.37 thf(func_def_26, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.78/0.37 thf(func_def_27, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.78/0.37 thf(func_def_28, type, pairwise: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > $o))).
% 0.78/0.37 thf(func_def_29, type, set_ord_atLeast: !>[X0: $tType]:((X0 > set @ X0))).
% 0.78/0.37 thf(func_def_30, type, set_or331188842AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.78/0.37 thf(func_def_31, type, set_or1433837966ssThan: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.78/0.37 thf(func_def_32, type, set_ord_atMost: !>[X0: $tType]:((X0 > set @ X0))).
% 0.78/0.37 thf(func_def_33, type, set_ord_greaterThan: !>[X0: $tType]:((X0 > set @ X0))).
% 0.78/0.37 thf(func_def_34, type, set_or1361889807AtMost: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.78/0.37 thf(func_def_35, type, set_or578182835ssThan: !>[X0: $tType]:((X0 > X0 > set @ X0))).
% 0.78/0.37 thf(func_def_36, type, set_ord_lessThan: !>[X0: $tType]:((X0 > set @ X0))).
% 0.78/0.37 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.78/0.37 thf(func_def_38, type, l1: set @ set @ a).
% 0.78/0.37 thf(func_def_39, type, l2: set @ set @ a).
% 0.78/0.37 thf(func_def_43, type, vAND: ($o > $o > $o)).
% 0.78/0.37 thf(func_def_44, type, db1: !>[X0: $tType]:(X0)).
% 0.78/0.37 thf(func_def_45, type, db0: !>[X0: $tType]:(X0)).
% 0.78/0.37 thf(func_def_46, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.78/0.37 thf(func_def_47, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.78/0.37 thf(func_def_48, type, vIMP: ($o > $o > $o)).
% 0.78/0.37 thf(func_def_49, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.78/0.37 thf(func_def_50, type, db3: !>[X0: $tType]:(X0)).
% 0.78/0.37 thf(func_def_51, type, db2: !>[X0: $tType]:(X0)).
% 0.78/0.37 thf(func_def_52, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.78/0.37 thf(func_def_53, type, vNOT: ($o > $o)).
% 0.78/0.37 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 0.78/0.37 thf(func_def_55, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.78/0.37 thf(func_def_56, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.78/0.37 thf(func_def_57, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.78/0.37 thf(func_def_58, type, sK3: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.78/0.37 thf(func_def_59, type, sK4: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_60, type, sK5: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_61, type, sK6: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_62, type, sK7: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_63, type, sK8: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_64, type, sK9: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_65, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_66, type, sK11: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_67, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_68, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_69, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_70, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_71, type, sK16: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_72, type, sK17: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_73, type, sK18: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_74, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_75, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_76, type, sK21: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_77, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_78, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_79, type, sK24: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_80, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_81, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_82, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_83, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_84, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_85, type, sK30: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_86, type, sK31: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_87, type, sK32: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.78/0.37 thf(func_def_88, type, sK33: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_89, type, sK34: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.78/0.37 thf(func_def_90, type, sK35: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.78/0.37 thf(func_def_91, type, sK36: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.78/0.37 thf(func_def_92, type, sK37: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.78/0.37 thf(func_def_93, type, sK38: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_94, type, sK39: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_95, type, sK40: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_96, type, sK41: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_97, type, sK42: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_98, type, sK43: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.78/0.37 thf(func_def_99, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_100, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_101, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_102, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.78/0.37 thf(func_def_103, type, sK48: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.78/0.37 thf(func_def_104, type, sK49: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.78/0.37 thf(func_def_105, type, sK50: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_106, type, sK51: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_107, type, sK52: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_108, type, sK53: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_109, type, sK54: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_110, type, sK55: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_111, type, sK56: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_112, type, sK57: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_113, type, sK58: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_114, type, sK59: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_115, type, sK60: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_116, type, sK61: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_117, type, sK62: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.78/0.37 thf(func_def_118, type, sK63: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_119, type, sK64: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_120, type, sK65: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_121, type, sK66: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_122, type, sK67: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_123, type, sK68: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_124, type, sK69: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_125, type, sK70: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_126, type, sK71: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_127, type, sK72: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_128, type, sK73: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.78/0.37 thf(func_def_129, type, sK74: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_130, type, sK75: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_131, type, sK76: !>[X0: $tType]:((X0 > X0))).
% 0.78/0.37 thf(func_def_132, type, sK77: set @ a).
% 0.78/0.37 thf(func_def_133, type, sK78: (set @ a > set @ a)).
% 0.78/0.37 thf(func_def_134, type, sK79: (set @ a > set @ a)).
% 0.78/0.37 thf(func_def_135, type, sK80: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.78/0.37 thf(func_def_136, type, sK81: !>[X0: $tType]:(((X0 > X0 > $o) > set @ X0 > X0))).
% 0.78/0.37 thf(func_def_137, type, sK82: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.78/0.37 thf(func_def_138, type, sK83: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 0.78/0.37 thf(func_def_139, type, sK84: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > set @ X0))).
% 0.78/0.37 thf(func_def_140, type, sK85: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > set @ X0))).
% 0.78/0.37 thf(func_def_141, type, sK86: !>[X0: $tType]:((set @ set @ X0 > set @ X0 > set @ X0))).
% 0.78/0.37 thf(func_def_142, type, sK87: !>[X0: $tType]:((set @ set @ X0 > set @ X0 > set @ X0))).
% 0.78/0.37 thf(func_def_143, type, sK88: !>[X0: $tType]:((set @ set @ X0 > set @ X0 > set @ X0))).
% 0.78/0.37 thf(func_def_144, type, sK89: !>[X0: $tType]:((set @ set @ X0 > set @ X0 > set @ X0))).
% 0.78/0.37 thf(func_def_145, type, sK90: !>[X0: $tType]:((set @ set @ X0 > set @ X0 > set @ X0))).
% 0.78/0.37 thf(f5,axiom,(
% 0.78/0.37 ! [X0 : $tType] : (gram_L608943123e_subs @ X0 = (^[X1 : set @ set @ X0, X2 : set @ set @ X0] : (! [X3 : set @ X0] : ((member @ set @ X0 @ X3 @ X2) => ? [X4 : set @ X0] : ((ord_less_eq @ set @ X0 @ X4 @ X3) & (member @ set @ X0 @ X4 @ X1))))))),
% 0.78/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_subs__def)).
% 0.78/0.37 thf(f276,axiom,(
% 0.78/0.37 (gram_L608943123e_subs @ a @ l2 @ l1) & (gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.78/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.78/0.37 thf(f277,conjecture,(
% 0.78/0.37 (gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.78/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
% 0.78/0.37 thf(f278,negated_conjecture,(
% 0.78/0.37 ~(gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.78/0.37 inference(negated_conjecture,[status(cth)],[f277])).
% 0.78/0.37 thf(f287,plain,(
% 0.78/0.37 ! [X0 : $tType] : (gram_L608943123e_subs @ X0 = (^[X1 : set @ set @ X0, X2 : set @ set @ X0] : (! [X3 : set @ X0] : ((member @ set @ X0 @ X3 @ X2) => ? [X4 : set @ X0] : ((ord_less_eq @ set @ X0 @ X4 @ X3) & (member @ set @ X0 @ X4 @ X1))))))),
% 0.78/0.37 inference(rectify,[],[f5])).
% 0.78/0.37 thf(f288,plain,(
% 0.78/0.37 ! [X0 : $tType] : (gram_L608943123e_subs @ X0 = (^[Y0 : set @ set @ X0]: ((^[Y1 : set @ set @ X0]: (!! @ set @ X0 @ (^[Y2 : set @ X0]: ((member @ set @ X0 @ Y2 @ Y1) => (?? @ set @ X0 @ (^[Y3 : set @ X0]: ((member @ set @ X0 @ Y3 @ Y0) & (ord_less_eq @ set @ X0 @ Y3 @ Y2)))))))))))),
% 0.78/0.37 inference(fool_elimination,[],[f287])).
% 0.78/0.37 thf(f816,plain,(
% 0.78/0.37 (gram_L608943123e_subs @ a @ l2 @ l1) & (gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.78/0.37 inference(rectify,[],[f276])).
% 0.78/0.37 thf(f817,plain,(
% 0.78/0.37 (((gram_L608943123e_subs @ a @ l2 @ l1)) = $true) & (((gram_L608943123e_subs @ a @ l1 @ l2)) = $true)),
% 0.78/0.37 inference(fool_elimination,[],[f816])).
% 0.78/0.37 thf(f818,plain,(
% 0.78/0.37 ~(gram_L608943123e_subs @ a @ l1 @ l2)),
% 0.78/0.37 inference(rectify,[],[f278])).
% 0.78/0.37 thf(f819,plain,(
% 0.78/0.37 ~ (((gram_L608943123e_subs @ a @ l1 @ l2)) = $true)),
% 0.78/0.37 inference(fool_elimination,[],[f818])).
% 0.78/0.37 thf(f851,plain,(
% 0.78/0.37 (((gram_L608943123e_subs @ a @ l1 @ l2)) != $true)),
% 0.78/0.37 inference(flattening,[],[f819])).
% 0.78/0.37 thf(f1236,plain,(
% 0.78/0.37 ( ! [X0 : $tType] : ((gram_L608943123e_subs @ X0 = (^[Y0 : set @ set @ X0]: ((^[Y1 : set @ set @ X0]: (!! @ set @ X0 @ (^[Y2 : set @ X0]: ((member @ set @ X0 @ Y2 @ Y1) => (?? @ set @ X0 @ (^[Y3 : set @ X0]: ((member @ set @ X0 @ Y3 @ Y0) & (ord_less_eq @ set @ X0 @ Y3 @ Y2)))))))))))) )),
% 0.78/0.37 inference(cnf_transformation,[],[f288])).
% 0.78/0.37 thf(f1568,plain,(
% 0.78/0.37 (((gram_L608943123e_subs @ a @ l1 @ l2)) = $true)),
% 0.78/0.37 inference(cnf_transformation,[],[f817])).
% 0.78/0.37 thf(f1570,plain,(
% 0.78/0.37 (((gram_L608943123e_subs @ a @ l1 @ l2)) != $true)),
% 0.78/0.37 inference(cnf_transformation,[],[f851])).
% 0.78/0.37 thf(f1579,plain,(
% 0.78/0.37 ($true = (((^[Y0 : set @ set @ a]: ((^[Y1 : set @ set @ a]: (!! @ set @ a @ (^[Y2 : set @ a]: ((member @ set @ a @ Y2 @ Y1) => (?? @ set @ a @ (^[Y3 : set @ a]: ((member @ set @ a @ Y3 @ Y0) & (ord_less_eq @ set @ a @ Y3 @ Y2)))))))))) @ l1 @ l2)))),
% 0.78/0.37 inference(definition_unfolding,[],[f1568,f1236])).
% 0.78/0.37 thf(f1580,plain,(
% 0.78/0.37 ($true != (((^[Y0 : set @ set @ a]: ((^[Y1 : set @ set @ a]: (!! @ set @ a @ (^[Y2 : set @ a]: ((member @ set @ a @ Y2 @ Y1) => (?? @ set @ a @ (^[Y3 : set @ a]: ((member @ set @ a @ Y3 @ Y0) & (ord_less_eq @ set @ a @ Y3 @ Y2)))))))))) @ l1 @ l2)))),
% 0.78/0.37 inference(definition_unfolding,[],[f1570,f1236])).
% 0.78/0.37 thf(f1607,plain,(
% 0.78/0.37 ($true != ((!! @ set @ a @ (^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l2) => (?? @ set @ a @ (^[Y1 : set @ a]: ((member @ set @ a @ Y1 @ l1) & (ord_less_eq @ set @ a @ Y1 @ Y0)))))))))),
% 0.78/0.37 inference(beta-eta_normalization,[],[f1580])).
% 0.78/0.37 thf(f1608,plain,(
% 0.78/0.37 ($false = (((^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l2) => (?? @ set @ a @ (^[Y1 : set @ a]: ((member @ set @ a @ Y1 @ l1) & (ord_less_eq @ set @ a @ Y1 @ Y0)))))) @ sK77)))),
% 0.78/0.37 inference(sigma_proxy_clausification,[],[f1607])).
% 0.78/0.37 thf(f1609,plain,(
% 0.78/0.37 ($false = (((member @ set @ a @ sK77 @ l2) => (?? @ set @ a @ (^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l1) & (ord_less_eq @ set @ a @ Y0 @ sK77)))))))),
% 0.78/0.37 inference(beta-eta_normalization,[],[f1608])).
% 0.78/0.37 thf(f1610,plain,(
% 0.78/0.37 ($false = ((?? @ set @ a @ (^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l1) & (ord_less_eq @ set @ a @ Y0 @ sK77))))))),
% 0.78/0.37 inference(imp_proxy_clausification,[],[f1609])).
% 0.78/0.37 thf(f1611,plain,(
% 0.78/0.37 ($true = ((member @ set @ a @ sK77 @ l2)))),
% 0.78/0.37 inference(imp_proxy_clausification,[],[f1609])).
% 0.78/0.37 thf(f1612,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($false = (((^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l1) & (ord_less_eq @ set @ a @ Y0 @ sK77))) @ X1)))) )),
% 0.78/0.37 inference(pi_proxy_clausification,[],[f1610])).
% 0.78/0.37 thf(f1613,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($false = (((member @ set @ a @ X1 @ l1) & (ord_less_eq @ set @ a @ X1 @ sK77))))) )),
% 0.78/0.37 inference(beta-eta_normalization,[],[f1612])).
% 0.78/0.37 thf(f1614,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($false = ((member @ set @ a @ X1 @ l1))) | ($false = ((ord_less_eq @ set @ a @ X1 @ sK77)))) )),
% 0.78/0.37 inference(and_proxy_clausification,[],[f1613])).
% 0.78/0.37 thf(f1615,plain,(
% 0.78/0.37 ($true = ((!! @ set @ a @ (^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l2) => (?? @ set @ a @ (^[Y1 : set @ a]: ((member @ set @ a @ Y1 @ l1) & (ord_less_eq @ set @ a @ Y1 @ Y0)))))))))),
% 0.78/0.37 inference(beta-eta_normalization,[],[f1579])).
% 0.78/0.37 thf(f1616,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($true = (((^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l2) => (?? @ set @ a @ (^[Y1 : set @ a]: ((member @ set @ a @ Y1 @ l1) & (ord_less_eq @ set @ a @ Y1 @ Y0)))))) @ X1)))) )),
% 0.78/0.37 inference(pi_proxy_clausification,[],[f1615])).
% 0.78/0.37 thf(f1617,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($true = (((member @ set @ a @ X1 @ l2) => (?? @ set @ a @ (^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l1) & (ord_less_eq @ set @ a @ Y0 @ X1)))))))) )),
% 0.78/0.37 inference(beta-eta_normalization,[],[f1616])).
% 0.78/0.37 thf(f1618,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($false = ((member @ set @ a @ X1 @ l2))) | ($true = ((?? @ set @ a @ (^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l1) & (ord_less_eq @ set @ a @ Y0 @ X1))))))) )),
% 0.78/0.37 inference(imp_proxy_clausification,[],[f1617])).
% 0.78/0.37 thf(f1619,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($false = ((member @ set @ a @ X1 @ l2))) | ($true = (((^[Y0 : set @ a]: ((member @ set @ a @ Y0 @ l1) & (ord_less_eq @ set @ a @ Y0 @ X1))) @ (sK78 @ X1))))) )),
% 0.78/0.37 inference(sigma_proxy_clausification,[],[f1618])).
% 0.78/0.37 thf(f1620,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($false = ((member @ set @ a @ X1 @ l2))) | ($true = (((member @ set @ a @ (sK78 @ X1) @ l1) & (ord_less_eq @ set @ a @ (sK78 @ X1) @ X1))))) )),
% 0.78/0.37 inference(beta-eta_normalization,[],[f1619])).
% 0.78/0.37 thf(f1621,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($true = ((ord_less_eq @ set @ a @ (sK78 @ X1) @ X1))) | ($false = ((member @ set @ a @ X1 @ l2)))) )),
% 0.78/0.37 inference(and_proxy_clausification,[],[f1620])).
% 0.78/0.37 thf(f1622,plain,(
% 0.78/0.37 ( ! [X1 : set @ a] : (($true = ((member @ set @ a @ (sK78 @ X1) @ l1))) | ($false = ((member @ set @ a @ X1 @ l2)))) )),
% 0.78/0.37 inference(and_proxy_clausification,[],[f1620])).
% 0.78/0.37 thf(f2659,plain,(
% 0.78/0.37 ( ! [X0 : set @ a] : (($true = $false) | ($false = ((ord_less_eq @ set @ a @ (sK78 @ X0) @ sK77))) | ($false = ((member @ set @ a @ X0 @ l2)))) )),
% 0.78/0.37 inference(constrained_superposition,[],[f1614,f1622])).
% 0.78/0.37 thf(f2660,plain,(
% 0.78/0.37 ( ! [X0 : set @ a] : (($false = ((ord_less_eq @ set @ a @ (sK78 @ X0) @ sK77))) | ($false = ((member @ set @ a @ X0 @ l2)))) )),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f2659])).
% 0.78/0.37 thf(f2762,plain,(
% 0.78/0.37 ($true = $false) | ($false = ((member @ set @ a @ sK77 @ l2))) | ($false = ((member @ set @ a @ sK77 @ l2)))),
% 0.78/0.37 inference(constrained_superposition,[],[f2660,f1621])).
% 0.78/0.37 thf(f2763,plain,(
% 0.78/0.37 ($true = $false) | ($false = ((member @ set @ a @ sK77 @ l2)))),
% 0.78/0.37 inference(duplicate_literal_removal,[],[f2762])).
% 0.78/0.37 thf(f2764,plain,(
% 0.78/0.37 ($false = ((member @ set @ a @ sK77 @ l2)))),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f2763])).
% 0.78/0.37 thf(f2772,plain,(
% 0.78/0.37 ($true = $false)),
% 0.78/0.37 inference(constrained_superposition,[],[f1611,f2764])).
% 0.78/0.37 thf(f2773,plain,(
% 0.78/0.37 $false),
% 0.78/0.37 inference(trivial_inequality_removal,[],[f2772])).
% 0.78/0.37 % SZS output end Proof for theBenchmark
% 0.78/0.37 % (3711080)------------------------------
% 0.78/0.37 % (3711080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.78/0.37 % (3711080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.78/0.37 % (3711080)CaDiCaL version: 2.1.3
% 0.78/0.37 % (3711080)Termination reason: Refutation
% 0.78/0.37 % (3711080)Time elapsed: 0.078 s
% 0.78/0.37 % (3711080)Peak memory usage: 14 MB
% 0.78/0.37 % (3711080)Instructions burned: 167 (million)
% 0.78/0.37 % (3711073)Success in time 0.132 s
% 0.78/0.37 % Vampire exiting
%------------------------------------------------------------------------------