%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP127^2 : 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 : n001.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 08:10:48 AM UTC 2026
% Result : Theorem 0.31s 0.47s
% Output : Refutation 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP127^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.26 % Computer : n001.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Tue Sep 29 20:03:21 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.25/0.32 Running first-order model finding
% 0.25/0.32 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
% 0.31/0.47 % (1741271)Will run a generic schedule for satisfiability detection.
% 0.31/0.47 % (1741281)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3480695980:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.31/0.47 % (1741278)% WARNING: option uhcvi not known.
% 0.31/0.47 % (1741277)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3949988078_2999 on theBenchmark for (2999ds/0Mi)
% 0.31/0.47 % (1741278)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4088816263:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.31/0.47 % (1741279)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=649629632:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.31/0.47 % (1741280)dis+10_1_sil=32000:sp=arity:random_seed=455594995:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.31/0.47 % (1741283)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2413888459:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.31/0.47 % (1741281)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.31/0.47 % (1741282)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4147652562:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.47 % (1741278)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.31/0.47 % (1741281)Instruction limit reached!
% 0.31/0.47 % (1741281)------------------------------
% 0.31/0.47 % (1741281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.47 % (1741281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.47 % (1741281)CaDiCaL version: 2.1.3
% 0.31/0.47 % (1741281)Termination reason: Instruction limit
% 0.31/0.47 % (1741281)Termination phase: Saturation
% 0.31/0.47 % (1741281)Time elapsed: 0.029 s
% 0.31/0.47 % (1741281)Peak memory usage: 13 MB
% 0.31/0.47 % (1741281)Instructions burned: 119 (million)
% 0.31/0.47 % (1741291)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2620984598:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.31/0.47 % Exception at run slice level
% 0.31/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.31/0.47 % (1741278)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.31/0.47 % (1741280)Instruction limit reached!
% 0.31/0.47 % (1741280)------------------------------
% 0.31/0.47 % (1741280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.47 % (1741280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.47 % (1741280)CaDiCaL version: 2.1.3
% 0.31/0.47 % (1741280)Termination reason: Instruction limit
% 0.31/0.47 % (1741280)Termination phase: Saturation
% 0.31/0.47 % (1741280)Time elapsed: 0.047 s
% 0.31/0.47 % (1741280)Peak memory usage: 13 MB
% 0.31/0.47 % (1741280)Instructions burned: 103 (million)
% 0.31/0.47 % Exception at run slice level
% 0.31/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.31/0.47 % (1741293)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2516487812:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.31/0.47 % (1741295)ott-21_1_sil=16000:fs=off:random_seed=1135878358:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.31/0.47 % (1741282)Instruction limit reached!
% 0.31/0.47 % (1741282)------------------------------
% 0.31/0.47 % (1741282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.47 % (1741282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.47 % (1741282)CaDiCaL version: 2.1.3
% 0.31/0.47 % (1741282)Termination reason: Instruction limit
% 0.31/0.47 % (1741282)Termination phase: Saturation
% 0.31/0.47 % (1741282)Time elapsed: 0.061 s
% 0.31/0.47 % (1741282)Peak memory usage: 13 MB
% 0.31/0.47 % (1741282)Instructions burned: 131 (million)
% 0.31/0.47 % (1741294)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=558529974:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.31/0.47 % (1741283)Instruction limit reached!
% 0.31/0.47 % (1741283)------------------------------
% 0.31/0.47 % (1741283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.47 % (1741283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.47 % (1741283)CaDiCaL version: 2.1.3
% 0.31/0.47 % (1741283)Termination reason: Instruction limit
% 0.31/0.47 % (1741283)Termination phase: Saturation
% 0.31/0.47 % (1741283)Time elapsed: 0.080 s
% 0.31/0.47 % (1741283)Peak memory usage: 14 MB
% 0.31/0.47 % (1741283)Instructions burned: 160 (million)
% 0.31/0.47 % (1741298)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2097644620:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.31/0.47 % (1741294)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.31/0.47 % (1741278) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1741271-1741278"...
% 0.31/0.47 % (1741301)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3732839694:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.31/0.47 % (1741278)...printing done.
% 0.31/0.47 % (1741278)Refutation found. Thanks to Tanya!
% 0.31/0.47 % SZS status Theorem for theBenchmark
% 0.31/0.47 % SZS output start Proof for theBenchmark
% 0.31/0.47 thf(type_def_5, type, monomo1453983439ondetT: ($tType * $tType) > $tType).
% 0.31/0.47 thf(type_def_6, type, countable_Set_cset: $tType > $tType).
% 0.31/0.47 thf(type_def_7, type, m: $tType).
% 0.31/0.47 thf(type_def_8, type, c: $tType).
% 0.31/0.47 thf(type_def_9, type, a: $tType).
% 0.31/0.47 thf(type_def_10, type, sTfun: ($tType * $tType) > $tType).
% 0.31/0.47 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_1, type, minus: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_2, type, bot: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_3, type, ord: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_5, type, group_add: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_6, type, no_bot: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_7, type, no_top: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_8, type, linorder: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_9, type, preorder: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_10, type, order_bot: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_11, type, wellorder: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_12, type, dense_order: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_13, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.31/0.47 thf(func_def_16, type, countable_Set_cin: !>[X0: $tType]:((X0 > countable_Set_cset @ X0 > $o))).
% 0.31/0.47 thf(func_def_17, type, counta2111716221insert: !>[X0: $tType]:((X0 > countable_Set_cset @ X0 > countable_Set_cset @ X0))).
% 0.31/0.47 thf(func_def_18, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 0.31/0.47 thf(func_def_19, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.31/0.47 thf(func_def_20, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.31/0.47 thf(func_def_21, type, monomo2011693592ondetM: !>[X0: $tType, X1: $tType, X2: $tType]:(((countable_Set_cset @ X0 > X1) > (X1 > (countable_Set_cset @ X0 > X1) > X1) > (countable_Set_cset @ X0 > (X0 > X1) > X1) > (countable_Set_cset @ X2 > (X2 > X1) > X1) > $o))).
% 0.31/0.47 thf(func_def_22, type, monomo759963067axioms: !>[X0: $tType, X1: $tType, X2: $tType]:(((countable_Set_cset @ X0 > X1) > (X1 > (countable_Set_cset @ X0 > X1) > X1) > (countable_Set_cset @ X0 > (X0 > X1) > X1) > (countable_Set_cset @ X2 > (X2 > X1) > X1) > $o))).
% 0.31/0.47 thf(func_def_23, type, monomo955616121nondet: !>[X0: $tType, X1: $tType, X2: $tType]:(((countable_Set_cset @ X0 > (X0 > X1) > X1) > countable_Set_cset @ X0 > (X0 > monomo1453983439ondetT @ X2 @ X1) > monomo1453983439ondetT @ X2 @ X1))).
% 0.31/0.47 thf(func_def_24, type, monomo439771545d_altc: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X1 > (X0 > X1) > X1) > (countable_Set_cset @ X2 > (X2 > X1) > X1) > $o))).
% 0.31/0.47 thf(func_def_25, type, monomo1425736922_altc3: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X1 > (X0 > X1) > X1) > (countable_Set_cset @ X2 > (X2 > X1) > X1) > $o))).
% 0.31/0.47 thf(func_def_26, type, monomo555039548axioms: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > (X1 > X0) > X0) > (countable_Set_cset @ X2 > (X2 > X0) > X0) > $o))).
% 0.31/0.47 thf(func_def_27, type, monomo109450930_state: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X1 > (X0 > X1) > X1) > ((X2 > X1) > X1) > (X2 > X1 > X1) > $o))).
% 0.31/0.47 thf(func_def_28, type, monomo1036387116e_altc: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X1 > (X0 > X1) > X1) > ((X2 > X1) > X1) > (X2 > X1 > X1) > (countable_Set_cset @ X3 > (X3 > X1) > X1) > $o))).
% 0.31/0.47 thf(func_def_29, type, monomo1324021455axioms: !>[X0: $tType, X1: $tType, X2: $tType]:((((X0 > X1) > X1) > (X0 > X1 > X1) > (countable_Set_cset @ X2 > (X2 > X1) > X1) > $o))).
% 0.31/0.47 thf(func_def_30, type, monomo410456285nondet: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1 > X1) > X0 > monomo1453983439ondetT @ X2 @ X1 > monomo1453983439ondetT @ X2 @ X1))).
% 0.31/0.47 thf(func_def_31, type, monomo1975189248ondetT: !>[X0: $tType, X1: $tType]:((X0 > monomo1453983439ondetT @ X1 @ X0))).
% 0.31/0.47 thf(func_def_32, type, monomo1564381680ondetT: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > monomo1453983439ondetT @ X2 @ X0 > X1))).
% 0.31/0.47 thf(func_def_33, type, monomo1291740684ondetT: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > monomo1453983439ondetT @ X2 @ X0 > X1))).
% 0.31/0.47 thf(func_def_34, type, monomo603716163nondet: !>[X0: $tType, X1: $tType]:((monomo1453983439ondetT @ X0 @ X1 > X1))).
% 0.31/0.47 thf(func_def_35, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.31/0.47 thf(func_def_36, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.47 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.47 thf(func_def_38, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_39, type, f: (c > monomo1453983439ondetT @ a @ m)).
% 0.31/0.47 thf(func_def_40, type, mergec: (countable_Set_cset @ c > (c > m) > m)).
% 0.31/0.47 thf(func_def_41, type, x: c).
% 0.31/0.47 thf(func_def_45, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.31/0.47 thf(func_def_46, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.31/0.47 thf(func_def_47, type, vOR: ($o > $o > $o)).
% 0.31/0.47 thf(func_def_48, type, vAND: ($o > $o > $o)).
% 0.31/0.47 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.31/0.47 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.31/0.47 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 0.31/0.47 thf(func_def_52, type, vNOT: ($o > $o)).
% 0.31/0.47 thf(func_def_53, type, vIMP: ($o > $o > $o)).
% 0.31/0.47 thf(func_def_54, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.47 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.31/0.47 thf(func_def_56, type, db4: !>[X0: $tType]:(X0)).
% 0.31/0.47 thf(func_def_57, type, db3: !>[X0: $tType]:(X0)).
% 0.31/0.47 thf(func_def_58, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.31/0.47 thf(func_def_59, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.31/0.47 thf(func_def_60, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.31/0.47 thf(func_def_61, type, sK3: !>[X0: $tType, X1: $tType]:((monomo1453983439ondetT @ X0 @ X1 > X1))).
% 0.31/0.47 thf(func_def_62, type, sK4: !>[X0: $tType, X1: $tType]:(((monomo1453983439ondetT @ X1 @ X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_63, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_64, type, sK6: !>[X0: $tType]:((countable_Set_cset @ X0 > countable_Set_cset @ X0 > X0))).
% 0.31/0.47 thf(func_def_65, type, sK7: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_66, type, sK8: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_67, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_68, type, sK10: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_69, type, sK11: !>[X0: $tType]:((countable_Set_cset @ X0 > countable_Set_cset @ X0 > X0))).
% 0.31/0.47 thf(func_def_70, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_71, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_72, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_73, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_74, type, sK16: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_75, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_76, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_77, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_78, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_79, type, sK21: !>[X0: $tType]:((countable_Set_cset @ X0 > X0))).
% 0.31/0.47 thf(func_def_80, type, sK22: !>[X0: $tType]:((countable_Set_cset @ X0 > X0 > countable_Set_cset @ X0))).
% 0.31/0.47 thf(func_def_81, type, sK23: !>[X0: $tType]:((countable_Set_cset @ X0 > X0 > countable_Set_cset @ X0))).
% 0.31/0.47 thf(func_def_82, type, sK24: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_83, type, sK25: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_84, type, sK26: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_85, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_86, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_87, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_88, type, sK30: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_89, type, sK31: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_90, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_91, type, sK33: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_92, type, sK34: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_93, type, sK35: !>[X0: $tType]:((X0 > X0))).
% 0.31/0.47 thf(func_def_94, type, sK36: !>[X0: $tType]:((X0 > X0))).
% 0.31/0.47 thf(func_def_95, type, sK37: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.31/0.47 thf(func_def_96, type, sK38: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_97, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_98, type, sK40: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_99, type, sK41: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_100, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_101, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.31/0.47 thf(func_def_102, type, sK44: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_103, type, sK45: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_104, type, sK46: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_105, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_106, type, sK48: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_107, type, sK49: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_108, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_109, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.31/0.47 thf(func_def_110, type, sK52: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.31/0.47 thf(func_def_111, type, sK53: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.31/0.47 thf(func_def_112, type, sK54: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.31/0.47 thf(func_def_113, type, sK55: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.31/0.47 thf(func_def_114, type, sK56: !>[X0: $tType]:((countable_Set_cset @ X0 > countable_Set_cset @ X0 > X0))).
% 0.31/0.47 thf(func_def_115, type, sK57: !>[X0: $tType]:((X0 > X0))).
% 0.31/0.47 thf(func_def_116, type, sK58: !>[X0: $tType]:((X0 > X0))).
% 0.31/0.47 thf(func_def_117, type, sK59: !>[X0: $tType]:((countable_Set_cset @ X0 > X0))).
% 0.31/0.47 thf(func_def_118, type, sK60: !>[X0: $tType]:((countable_Set_cset @ X0 > X0))).
% 0.31/0.47 thf(func_def_119, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > (X1 > X0) > X1))).
% 0.31/0.47 thf(func_def_120, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X0) > (X1 > X0) > X1 > X2))).
% 0.31/0.47 thf(func_def_121, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > (X2 > X1) > (X0 > X1) > X2))).
% 0.31/0.47 thf(func_def_122, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X0 > X2) > X0))).
% 0.31/0.47 thf(func_def_123, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X0 > X2) > X1 > X2))).
% 0.31/0.47 thf(func_def_124, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X0 > X2) > X0))).
% 0.31/0.47 thf(f1,axiom,(
% 0.31/0.47 ! [X7 : c,X8 : (c > m)] : (((mergec @ (counta2111716221insert @ c @ X7 @ bot_bot @ countable_Set_cset @ c) @ X8)) = ((X8 @ X7)))),
% 0.31/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_mergec__single)).
% 0.31/0.47 thf(f18,axiom,(
% 0.31/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (comp @ X2 @ X1 @ X0 = (^[X3 : (X2 > X1), X4 : (X0 > X2), X5 : X0] : ((X3 @ (X4 @ X5)))))),
% 0.31/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_comp__apply)).
% 0.31/0.47 thf(f19,axiom,(
% 0.31/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (monomo955616121nondet @ X2 @ X1 @ X0 = (^[X3 : (countable_Set_cset @ X2 > (X2 > X1) > X1), X4 : countable_Set_cset @ X2, X5 : (X2 > monomo1453983439ondetT @ X0 @ X1)] : ((monomo1975189248ondetT @ X1 @ X0 @ (X3 @ X4 @ (comp @ monomo1453983439ondetT @ X0 @ X1 @ X1 @ X2 @ monomo603716163nondet @ X0 @ X1 @ X5))))))),
% 0.31/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_cset__nondetM__base_Oaltc__nondet__def)).
% 0.31/0.47 thf(f29,axiom,(
% 0.31/0.47 ! [X0 : $tType,X1 : $tType,X2 : monomo1453983439ondetT @ X1 @ X0] : (((monomo1975189248ondetT @ X0 @ X1 @ (monomo603716163nondet @ X1 @ X0 @ X2))) = X2)),
% 0.31/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_nondetT_Ocollapse)).
% 0.31/0.47 thf(f279,conjecture,(
% 0.31/0.47 (((monomo955616121nondet @ c @ m @ a @ mergec @ (counta2111716221insert @ c @ x @ bot_bot @ countable_Set_cset @ c) @ f)) = ((f @ x)))),
% 0.31/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.31/0.47 thf(f280,negated_conjecture,(
% 0.31/0.47 ~ (((monomo955616121nondet @ c @ m @ a @ mergec @ (counta2111716221insert @ c @ x @ bot_bot @ countable_Set_cset @ c) @ f)) = ((f @ x)))),
% 0.31/0.47 inference(negated_conjecture,[status(cth)],[f279])).
% 0.31/0.47 thf(f294,plain,(
% 0.31/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (comp @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1]: ((^[Y1 : X0 > X2]: ((^[Y2 : X0]: (Y0 @ (Y1 @ Y2))))))))),
% 0.31/0.47 inference(fool_elimination,[],[f18])).
% 0.31/0.47 thf(f295,plain,(
% 0.31/0.47 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (monomo955616121nondet @ X2 @ X1 @ X0 = (^[Y0 : countable_Set_cset @ X2 > (X2 > X1) > X1]: ((^[Y1 : countable_Set_cset @ X2]: ((^[Y2 : X2 > monomo1453983439ondetT @ X0 @ X1]: (monomo1975189248ondetT @ X1 @ X0 @ (Y0 @ Y1 @ (comp @ monomo1453983439ondetT @ X0 @ X1 @ X1 @ X2 @ monomo603716163nondet @ X0 @ X1 @ Y2)))))))))),
% 0.31/0.47 inference(fool_elimination,[],[f19])).
% 0.31/0.47 thf(f742,plain,(
% 0.31/0.47 ! [X0 : c,X1 : (c > m)] : (((mergec @ (counta2111716221insert @ c @ X0 @ bot_bot @ countable_Set_cset @ c) @ X1)) = ((X1 @ X0)))),
% 0.31/0.47 inference(rectify,[],[f1])).
% 0.31/0.47 thf(f778,plain,(
% 0.31/0.47 (((monomo955616121nondet @ c @ m @ a @ mergec @ (counta2111716221insert @ c @ x @ bot_bot @ countable_Set_cset @ c) @ f)) != ((f @ x)))),
% 0.31/0.47 inference(flattening,[],[f280])).
% 0.31/0.47 thf(f1094,plain,(
% 0.31/0.47 ( ! [X0 : c,X1 : (c > m)] : ((((mergec @ (counta2111716221insert @ c @ X0 @ bot_bot @ countable_Set_cset @ c) @ X1)) = ((X1 @ X0)))) )),
% 0.31/0.47 inference(cnf_transformation,[],[f742])).
% 0.31/0.47 thf(f1111,plain,(
% 0.31/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((comp @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1]: ((^[Y1 : X0 > X2]: ((^[Y2 : X0]: (Y0 @ (Y1 @ Y2))))))))) )),
% 0.31/0.47 inference(cnf_transformation,[],[f294])).
% 0.31/0.47 thf(f1112,plain,(
% 0.31/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((monomo955616121nondet @ X2 @ X1 @ X0 = (^[Y0 : countable_Set_cset @ X2 > (X2 > X1) > X1]: ((^[Y1 : countable_Set_cset @ X2]: ((^[Y2 : X2 > monomo1453983439ondetT @ X0 @ X1]: (monomo1975189248ondetT @ X1 @ X0 @ (Y0 @ Y1 @ (comp @ monomo1453983439ondetT @ X0 @ X1 @ X1 @ X2 @ monomo603716163nondet @ X0 @ X1 @ Y2)))))))))) )),
% 0.31/0.47 inference(cnf_transformation,[],[f295])).
% 0.31/0.47 thf(f1122,plain,(
% 0.31/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : monomo1453983439ondetT @ X1 @ X0] : ((((monomo1975189248ondetT @ X0 @ X1 @ (monomo603716163nondet @ X1 @ X0 @ X2))) = X2)) )),
% 0.31/0.47 inference(cnf_transformation,[],[f29])).
% 0.31/0.47 thf(f1427,plain,(
% 0.31/0.47 (((monomo955616121nondet @ c @ m @ a @ mergec @ (counta2111716221insert @ c @ x @ bot_bot @ countable_Set_cset @ c) @ f)) != ((f @ x)))),
% 0.31/0.47 inference(cnf_transformation,[],[f778])).
% 0.31/0.47 thf(f1430,plain,(
% 0.31/0.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((monomo955616121nondet @ X2 @ X1 @ X0 = (^[Y0 : countable_Set_cset @ X2 > (X2 > X1) > X1]: ((^[Y1 : countable_Set_cset @ X2]: ((^[Y2 : X2 > monomo1453983439ondetT @ X0 @ X1]: (monomo1975189248ondetT @ X1 @ X0 @ (Y0 @ Y1 @ ((^[Y3 : monomo1453983439ondetT @ X0 @ X1 > X1]: ((^[Y4 : X2 > monomo1453983439ondetT @ X0 @ X1]: ((^[Y5 : X2]: (Y3 @ (Y4 @ Y5))))))) @ monomo603716163nondet @ X0 @ X1 @ Y2)))))))))) )),
% 0.31/0.47 inference(definition_unfolding,[],[f1112,f1111])).
% 0.31/0.47 thf(f1460,plain,(
% 0.31/0.47 (((f @ x)) != (((^[Y0 : countable_Set_cset @ c > (c > m) > m]: ((^[Y1 : countable_Set_cset @ c]: ((^[Y2 : c > monomo1453983439ondetT @ a @ m]: (monomo1975189248ondetT @ m @ a @ (Y0 @ Y1 @ ((^[Y3 : monomo1453983439ondetT @ a @ m > m]: ((^[Y4 : c > monomo1453983439ondetT @ a @ m]: ((^[Y5 : c]: (Y3 @ (Y4 @ Y5))))))) @ monomo603716163nondet @ a @ m @ Y2)))))))) @ mergec @ (counta2111716221insert @ c @ x @ bot_bot @ countable_Set_cset @ c) @ f)))),
% 0.31/0.47 inference(definition_unfolding,[],[f1427,f1430])).
% 0.31/0.47 thf(f1497,plain,(
% 0.31/0.47 (((f @ x)) != ((monomo1975189248ondetT @ m @ a @ (mergec @ (counta2111716221insert @ c @ x @ bot_bot @ countable_Set_cset @ c) @ (^[Y0 : c]: (monomo603716163nondet @ a @ m @ (f @ Y0)))))))),
% 0.31/0.47 inference(beta-eta_normalization,[],[f1460])).
% 0.31/0.47 thf(f3107,plain,(
% 0.31/0.47 (((f @ x)) != ((monomo1975189248ondetT @ m @ a @ ((^[Y0 : c]: (monomo603716163nondet @ a @ m @ (f @ Y0))) @ x))))),
% 0.31/0.47 inference(constrained_superposition,[],[f1497,f1094])).
% 0.31/0.47 thf(f3108,plain,(
% 0.31/0.47 (((f @ x)) != ((monomo1975189248ondetT @ m @ a @ (monomo603716163nondet @ a @ m @ (f @ x)))))),
% 0.31/0.47 inference(beta-eta_normalization,[],[f3107])).
% 0.31/0.47 thf(f3109,plain,(
% 0.31/0.47 $false),
% 0.31/0.47 inference(forward_subsumption_resolution,[],[f3108,f1122])).
% 0.31/0.47 % SZS output end Proof for theBenchmark
% 0.31/0.47 % (1741278)------------------------------
% 0.31/0.47 % (1741278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.47 % (1741278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.47 % (1741278)CaDiCaL version: 2.1.3
% 0.31/0.47 % (1741278)Termination reason: Refutation
% 0.31/0.47 % (1741278)Time elapsed: 0.100 s
% 0.31/0.47 % (1741278)Peak memory usage: 14 MB
% 0.31/0.47 % (1741278)Instructions burned: 191 (million)
% 0.31/0.47 % (1741271)Success in time 0.138 s
% 0.31/0.47 % Vampire exiting
%------------------------------------------------------------------------------