%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP033^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 08:10:26 AM UTC 2026
% Result : Theorem 0.89s 0.40s
% Output : Refutation 0.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP033^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 19:41:49 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.89/0.40 % (1085211)Will run a generic schedule for satisfiability detection.
% 0.89/0.40 % (1085219)dis+10_1_sil=32000:sp=arity:random_seed=983519736:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.89/0.40 % (1085217)% WARNING: option uhcvi not known.
% 0.89/0.40 % (1085216)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2755899748_2999 on theBenchmark for (2999ds/0Mi)
% 0.89/0.40 % (1085217)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4285411117:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.89/0.40 % (1085218)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=922965881:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.89/0.40 % (1085220)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1573582670:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.89/0.40 % (1085217)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.89/0.40 % (1085219)Instruction limit reached!
% 0.89/0.40 % (1085219)------------------------------
% 0.89/0.40 % (1085219)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.40 % (1085219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.40 % (1085219)CaDiCaL version: 2.1.3
% 0.89/0.40 % (1085219)Termination reason: Instruction limit
% 0.89/0.40 % (1085219)Termination phase: Saturation
% 0.89/0.40 % (1085219)Time elapsed: 0.024 s
% 0.89/0.40 % (1085219)Peak memory usage: 13 MB
% 0.89/0.40 % (1085219)Instructions burned: 104 (million)
% 0.89/0.40 % (1085220)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.89/0.40 % (1085222)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1097499565:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.89/0.40 % (1085221)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3152431815:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.89/0.40 % (1085228)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=4019602447:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.89/0.40 % Exception at run slice level
% 0.89/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.89/0.40 % (1085217)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.89/0.40 % Exception at run slice level
% 0.89/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.89/0.40 % (1085232)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=257190418:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.89/0.40 % (1085220)Instruction limit reached!
% 0.89/0.40 % (1085220)------------------------------
% 0.89/0.40 % (1085220)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.40 % (1085220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.40 % (1085220)CaDiCaL version: 2.1.3
% 0.89/0.40 % (1085220)Termination reason: Instruction limit
% 0.89/0.40 % (1085220)Termination phase: Saturation
% 0.89/0.40 % (1085220)Time elapsed: 0.054 s
% 0.89/0.40 % (1085220)Peak memory usage: 13 MB
% 0.89/0.40 % (1085220)Instructions burned: 116 (million)
% 0.89/0.40 % (1085233)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=549509311:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.89/0.40 % (1085233)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.89/0.40 % (1085233)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.89/0.40 % (1085236)ott-21_1_sil=16000:fs=off:random_seed=2720199873:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.89/0.40 % (1085222)Instruction limit reached!
% 0.89/0.40 % (1085222)------------------------------
% 0.89/0.40 % (1085222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.40 % (1085222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.40 % (1085222)CaDiCaL version: 2.1.3
% 0.89/0.40 % (1085222)Termination reason: Instruction limit
% 0.89/0.40 % (1085222)Termination phase: Saturation
% 0.89/0.40 % (1085222)Time elapsed: 0.075 s
% 0.89/0.40 % (1085222)Peak memory usage: 13 MB
% 0.89/0.40 % (1085222)Instructions burned: 160 (million)
% 0.89/0.40 % (1085221)Instruction limit reached!
% 0.89/0.40 % (1085221)------------------------------
% 0.89/0.40 % (1085221)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.40 % (1085221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.40 % (1085221)CaDiCaL version: 2.1.3
% 0.89/0.40 % (1085221)Termination reason: Instruction limit
% 0.89/0.40 % (1085221)Termination phase: Saturation
% 0.89/0.40 % (1085221)Time elapsed: 0.080 s
% 0.89/0.40 % (1085221)Peak memory usage: 13 MB
% 0.89/0.40 % (1085221)Instructions burned: 132 (million)
% 0.89/0.40 % (1085238)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2825137712:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.89/0.40 % (1085232)Instruction limit reached!
% 0.89/0.40 % (1085232)------------------------------
% 0.89/0.40 % (1085232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.40 % (1085232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.40 % (1085232)CaDiCaL version: 2.1.3
% 0.89/0.40 % (1085232)Termination reason: Instruction limit
% 0.89/0.40 % (1085232)Termination phase: Saturation
% 0.89/0.40 % (1085232)Time elapsed: 0.062 s
% 0.89/0.40 % (1085232)Peak memory usage: 13 MB
% 0.89/0.40 % (1085232)Instructions burned: 132 (million)
% 0.89/0.40 % (1085239)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1647140764:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.89/0.40 % (1085233) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1085211-1085233"...
% 0.89/0.40 % (1085233)...printing done.
% 0.89/0.40 % (1085233)Refutation found. Thanks to Tanya!
% 0.89/0.40 % SZS status Theorem for theBenchmark
% 0.89/0.40 % SZS output start Proof for theBenchmark
% 0.89/0.40 thf(type_def_5, type, binary1291135688e_Tree: $tType > $tType).
% 0.89/0.40 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 0.89/0.40 thf(type_def_7, type, set: $tType > $tType).
% 0.89/0.40 thf(type_def_8, type, int: $tType).
% 0.89/0.40 thf(type_def_9, type, a: $tType).
% 0.89/0.40 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.89/0.40 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_1, type, bot: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_2, type, ord: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_4, type, no_bot: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_5, type, no_top: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_7, type, preorder: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_8, type, order_bot: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_9, type, wellorder: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_10, type, dense_order: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_11, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_12, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_13, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.89/0.40 thf(func_def_14, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X0 > X1) > $o))).
% 0.89/0.40 thf(func_def_15, type, binary210054475elle_T: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.89/0.40 thf(func_def_16, type, binary1746293266le_Tip: !>[X0: $tType]:(binary1291135688e_Tree @ X0)).
% 0.89/0.40 thf(func_def_17, type, binary536355927e_Tree: !>[X0: $tType, X1: $tType]:((X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0) > binary1291135688e_Tree @ X1 > X0))).
% 0.89/0.41 thf(func_def_18, type, binary1929596613c_Tree: !>[X0: $tType, X1: $tType]:((X0 > (binary1291135688e_Tree @ X1 > X1 > binary1291135688e_Tree @ X1 > X0 > X0 > X0) > binary1291135688e_Tree @ X1 > X0))).
% 0.89/0.41 thf(func_def_19, type, binary1830089824insert: !>[X0: $tType]:(((X0 > int) > X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.89/0.41 thf(func_def_20, type, binary827270440e_memb: !>[X0: $tType]:(((X0 > int) > X0 > binary1291135688e_Tree @ X0 > $o))).
% 0.89/0.41 thf(func_def_21, type, binary997842527remove: !>[X0: $tType]:(((X0 > int) > X0 > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.89/0.41 thf(func_def_22, type, binary576689334lle_rm: !>[X0: $tType]:(((X0 > int) > binary1291135688e_Tree @ X0 > X0))).
% 0.89/0.41 thf(func_def_23, type, binary1653327646_setOf: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > set @ X0))).
% 0.89/0.41 thf(func_def_24, type, binary1610619414edTree: !>[X0: $tType]:(((X0 > int) > binary1291135688e_Tree @ X0 > $o))).
% 0.89/0.41 thf(func_def_25, type, binary231205461t_pred: !>[X0: $tType]:(((X0 > int) > X0 > X0 > binary1291135688e_Tree @ X0 > $o))).
% 0.89/0.41 thf(func_def_26, type, binary213313527le_wrm: !>[X0: $tType]:(((X0 > int) > binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.89/0.41 thf(func_def_27, type, binary1271298290_wrmrm: !>[X0: $tType]:(((X0 > int) > binary1291135688e_Tree @ X0 > product_prod @ binary1291135688e_Tree @ X0 @ X0))).
% 0.89/0.41 thf(func_def_28, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.89/0.41 thf(func_def_29, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.89/0.41 thf(func_def_30, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.89/0.41 thf(func_def_31, type, ordering_top: !>[X0: $tType]:(((X0 > X0 > $o) > (X0 > X0 > $o) > X0 > $o))).
% 0.89/0.41 thf(func_def_32, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.89/0.41 thf(func_def_33, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2))).
% 0.89/0.41 thf(func_def_34, type, inv_image: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X0 @ X0 > (X1 > X0) > set @ product_prod @ X1 @ X1))).
% 0.89/0.41 thf(func_def_35, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.89/0.41 thf(func_def_36, type, is_empty: !>[X0: $tType]:((set @ X0 > $o))).
% 0.89/0.41 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.89/0.41 thf(func_def_38, type, h: (a > int)).
% 0.89/0.41 thf(func_def_39, type, t1: binary1291135688e_Tree @ a).
% 0.89/0.41 thf(func_def_40, type, t2: binary1291135688e_Tree @ a).
% 0.89/0.41 thf(func_def_41, type, x: a).
% 0.89/0.41 thf(func_def_45, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.89/0.41 thf(func_def_46, type, vAND: ($o > $o > $o)).
% 0.89/0.41 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 0.89/0.41 thf(func_def_48, type, db3: !>[X0: $tType]:(X0)).
% 0.89/0.41 thf(func_def_49, type, db0: !>[X0: $tType]:(X0)).
% 0.89/0.41 thf(func_def_50, type, db2: !>[X0: $tType]:(X0)).
% 0.89/0.41 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 0.89/0.41 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.89/0.41 thf(func_def_53, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.89/0.41 thf(func_def_54, type, vNOT: ($o > $o)).
% 0.89/0.41 thf(func_def_55, type, vOR: ($o > $o > $o)).
% 0.89/0.41 thf(func_def_56, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.89/0.41 thf(func_def_57, type, db4: !>[X0: $tType]:(X0)).
% 0.89/0.41 thf(func_def_58, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.89/0.41 thf(func_def_59, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.89/0.41 thf(func_def_60, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.89/0.41 thf(func_def_61, type, sK3: !>[X0: $tType]:(((binary1291135688e_Tree @ X0 > $o) > binary1291135688e_Tree @ X0))).
% 0.89/0.41 thf(func_def_62, type, sK4: !>[X0: $tType]:(((binary1291135688e_Tree @ X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_63, type, sK5: !>[X0: $tType]:(((binary1291135688e_Tree @ X0 > $o) > binary1291135688e_Tree @ X0))).
% 0.89/0.41 thf(func_def_64, type, sK6: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.89/0.41 thf(func_def_65, type, sK7: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > X0))).
% 0.89/0.41 thf(func_def_66, type, sK8: !>[X0: $tType]:((binary1291135688e_Tree @ X0 > binary1291135688e_Tree @ X0))).
% 0.89/0.41 thf(func_def_67, type, sK9: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.89/0.41 thf(func_def_68, type, sK10: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_69, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_70, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_71, type, sK13: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_72, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_73, type, sK15: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_74, type, sK16: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_75, type, sK17: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_76, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_77, type, sK19: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_78, type, sK20: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_79, type, sK21: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_80, type, sK22: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_81, type, sK23: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_82, type, sK24: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_83, type, sK25: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_84, type, sK26: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_85, type, sK27: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_86, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_87, type, sK29: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_88, type, sK30: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_89, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_90, type, sK32: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_91, type, sK33: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_92, type, sK34: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_93, type, sK35: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.89/0.41 thf(func_def_94, type, sK36: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_95, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_96, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_97, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_98, type, sK40: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_99, type, sK41: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_100, type, sK42: !>[X0: $tType]:((set @ X0 > X0))).
% 0.89/0.41 thf(func_def_101, type, sK43: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_102, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_103, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_104, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_105, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_106, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_107, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_108, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_109, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.89/0.41 thf(func_def_110, type, sK52: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.89/0.41 thf(func_def_111, type, sK53: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.89/0.41 thf(func_def_112, type, sK54: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.89/0.41 thf(func_def_113, type, sK55: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.89/0.41 thf(func_def_114, type, sK56: !>[X0: $tType]:((set @ X0 > X0))).
% 0.89/0.41 thf(func_def_115, type, sK57: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_116, type, sK58: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_117, type, sK59: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_118, type, sK60: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_119, type, sK61: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.89/0.41 thf(func_def_120, type, sK62: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.89/0.41 thf(func_def_121, type, sK63: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_122, type, sK64: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_123, type, sK65: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_124, type, sK66: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_125, type, sK67: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_126, type, sK68: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_127, type, sK69: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_128, type, sK70: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_129, type, sK71: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_130, type, sK72: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_131, type, sK73: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_132, type, sK74: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.89/0.41 thf(func_def_133, type, sK75: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_134, type, sK76: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_135, type, sK77: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_136, type, sK78: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_137, type, sK79: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_138, type, sK80: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_139, type, sK81: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_140, type, sK82: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_141, type, sK83: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_142, type, sK84: !>[X0: $tType]:((X0 > X0))).
% 0.89/0.41 thf(func_def_143, type, sK85: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.89/0.41 thf(func_def_144, type, sK86: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_145, type, sK87: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 0.89/0.41 thf(func_def_146, type, sK88: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.89/0.41 thf(func_def_147, type, sK89: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.89/0.41 thf(func_def_148, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X2))).
% 0.89/0.41 thf(func_def_149, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X1))).
% 0.89/0.41 thf(func_def_150, type, sK92: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X1))).
% 0.89/0.41 thf(func_def_151, type, sK93: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > (X1 > X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_152, type, sK94: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1))).
% 0.89/0.41 thf(func_def_153, type, sK95: !>[X0: $tType, X1: $tType]:(((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0))).
% 0.89/0.41 thf(func_def_154, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0))).
% 0.89/0.41 thf(func_def_155, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1))).
% 0.89/0.41 thf(func_def_156, type, sK98: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0))).
% 0.89/0.41 thf(func_def_157, type, sK99: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1))).
% 0.89/0.41 thf(func_def_158, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1))).
% 0.89/0.41 thf(func_def_159, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0))).
% 0.89/0.41 thf(func_def_160, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0))).
% 0.89/0.41 thf(func_def_161, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2))).
% 0.89/0.41 thf(func_def_162, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2))).
% 0.89/0.41 thf(func_def_163, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:(((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1))).
% 0.89/0.41 thf(func_def_164, type, sK106: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 0.89/0.41 thf(func_def_165, type, sK107: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_166, type, sK108: !>[X0: $tType]:((set @ X0 > X0))).
% 0.89/0.41 thf(func_def_167, type, sK109: !>[X0: $tType]:((set @ X0 > X0))).
% 0.89/0.41 thf(func_def_168, type, sK110: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_169, type, sK111: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.89/0.41 thf(func_def_170, type, sK112: !>[X0: $tType]:(((X0 > int) > X0 > binary1291135688e_Tree @ X0 > X0))).
% 0.89/0.41 thf(func_def_171, type, sK113: !>[X0: $tType]:(((X0 > int) > binary1291135688e_Tree @ X0 > X0 > X0))).
% 0.89/0.41 thf(func_def_173, type, sK115: !>[X0: $tType]:(((X0 > a > int) > X0 > a))).
% 0.89/0.41 thf(func_def_174, type, sK116: !>[X0: $tType]:(((X0 > a > int) > X0 > a))).
% 0.89/0.41 thf(f2,axiom,(
% 0.89/0.41 (binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2))),
% 0.89/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_s)).
% 0.89/0.41 thf(f4,axiom,(
% 0.89/0.41 ! [X0 : $tType,X1 : (X0 > int),X2 : binary1291135688e_Tree @ X0,X3 : X0,X4 : binary1291135688e_Tree @ X0] : ((binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)) => (binary1610619414edTree @ X0 @ X1 @ X2))),
% 0.89/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_sortLemmaL)).
% 0.89/0.41 thf(f280,conjecture,(
% 0.89/0.41 (binary1610619414edTree @ a @ h @ t1)),
% 0.89/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.89/0.41 thf(f281,negated_conjecture,(
% 0.89/0.41 ~(binary1610619414edTree @ a @ h @ t1)),
% 0.89/0.41 inference(negated_conjecture,[status(cth)],[f280])).
% 0.89/0.41 thf(f282,plain,(
% 0.89/0.41 (binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2))),
% 0.89/0.41 inference(rectify,[],[f2])).
% 0.89/0.41 thf(f283,plain,(
% 0.89/0.41 (((binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2))) = $true)),
% 0.89/0.41 inference(fool_elimination,[],[f282])).
% 0.89/0.41 thf(f284,plain,(
% 0.89/0.41 ! [X0 : $tType,X1 : (X0 > int),X2 : binary1291135688e_Tree @ X0,X3 : X0,X4 : binary1291135688e_Tree @ X0] : ((binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4)) => (binary1610619414edTree @ X0 @ X1 @ X2))),
% 0.89/0.41 inference(rectify,[],[f4])).
% 0.89/0.41 thf(f285,plain,(
% 0.89/0.41 ! [X0 : $tType,X1 : (X0 > int),X2 : binary1291135688e_Tree @ X0,X3 : X0,X4 : binary1291135688e_Tree @ X0] : ((((binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4))) = $true) => (((binary1610619414edTree @ X0 @ X1 @ X2)) = $true))),
% 0.89/0.41 inference(fool_elimination,[],[f284])).
% 0.89/0.41 thf(f792,plain,(
% 0.89/0.41 ~(binary1610619414edTree @ a @ h @ t1)),
% 0.89/0.41 inference(rectify,[],[f281])).
% 0.89/0.41 thf(f793,plain,(
% 0.89/0.41 ~ (((binary1610619414edTree @ a @ h @ t1)) = $true)),
% 0.89/0.41 inference(fool_elimination,[],[f792])).
% 0.89/0.41 thf(f832,plain,(
% 0.89/0.41 (((binary1610619414edTree @ a @ h @ t1)) != $true)),
% 0.89/0.41 inference(flattening,[],[f793])).
% 0.89/0.41 thf(f833,plain,(
% 0.89/0.41 ! [X0 : $tType,X1 : (X0 > int),X2 : binary1291135688e_Tree @ X0,X3 : X0,X4 : binary1291135688e_Tree @ X0] : ((((binary1610619414edTree @ X0 @ X1 @ X2)) = $true) | (((binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4))) != $true))),
% 0.89/0.41 inference(ennf_transformation,[],[f285])).
% 0.89/0.41 thf(f1185,plain,(
% 0.89/0.41 (((binary1610619414edTree @ a @ h @ (binary210054475elle_T @ a @ t1 @ x @ t2))) = $true)),
% 0.89/0.41 inference(cnf_transformation,[],[f283])).
% 0.89/0.41 thf(f1187,plain,(
% 0.89/0.41 ( ! [X0 : $tType,X2 : binary1291135688e_Tree @ X0,X3 : X0,X1 : (X0 > int),X4 : binary1291135688e_Tree @ X0] : ((((binary1610619414edTree @ X0 @ X1 @ (binary210054475elle_T @ X0 @ X2 @ X3 @ X4))) != $true) | (((binary1610619414edTree @ X0 @ X1 @ X2)) = $true)) )),
% 0.89/0.41 inference(cnf_transformation,[],[f833])).
% 0.89/0.41 thf(f1544,plain,(
% 0.89/0.41 (((binary1610619414edTree @ a @ h @ t1)) != $true)),
% 0.89/0.41 inference(cnf_transformation,[],[f832])).
% 0.89/0.41 thf(f3620,plain,(
% 0.89/0.41 ($true != $true) | (((binary1610619414edTree @ a @ h @ t1)) = $true)),
% 0.89/0.41 inference(constrained_superposition,[],[f1187,f1185])).
% 0.89/0.41 thf(f3641,plain,(
% 0.89/0.41 (((binary1610619414edTree @ a @ h @ t1)) = $true)),
% 0.89/0.41 inference(trivial_inequality_removal,[],[f3620])).
% 0.89/0.41 thf(f3644,plain,(
% 0.89/0.41 $false),
% 0.89/0.41 inference(forward_subsumption_resolution,[],[f3641,f1544])).
% 0.89/0.41 % SZS output end Proof for theBenchmark
% 0.89/0.41 % (1085233)------------------------------
% 0.89/0.41 % (1085233)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.89/0.41 % (1085233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.89/0.41 % (1085233)CaDiCaL version: 2.1.3
% 0.89/0.41 % (1085233)Termination reason: Refutation
% 0.89/0.41 % (1085233)Time elapsed: 0.077 s
% 0.89/0.41 % (1085233)Peak memory usage: 15 MB
% 0.89/0.41 % (1085233)Instructions burned: 292 (million)
% 0.89/0.41 % (1085211)Success in time 0.184 s
% 0.89/0.41 % Vampire exiting
%------------------------------------------------------------------------------