%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL733^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:15:10 AM UTC 2026
% Result : Theorem 1.88s 0.80s
% Output : Refutation 1.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL733^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n011.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 10:05:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 1.88/0.80 % (4082264)Will run a generic schedule for satisfiability detection.
% 1.88/0.80 % (4082269)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2001534444_2999 on theBenchmark for (2999ds/0Mi)
% 1.88/0.80 % Exception at run slice level
% 1.88/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.88/0.80 % (4082270)% WARNING: option uhcvi not known.
% 1.88/0.80 % (4082270)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1565109318:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.88/0.80 % (4082270)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.88/0.80 % (4082270)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.88/0.80 % (4082277)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3391609684:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.88/0.80 % Exception at run slice level
% 1.88/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.88/0.80 % (4082280)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=230074696:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.88/0.80 % (4082272)dis+10_1_sil=32000:sp=arity:random_seed=1000930466:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.88/0.80 % (4082280)Instruction limit reached!
% 1.88/0.80 % (4082280)------------------------------
% 1.88/0.80 % (4082280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082280)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082280)Termination reason: Instruction limit
% 1.88/0.80 % (4082280)Termination phase: Saturation
% 1.88/0.80 % (4082280)Time elapsed: 0.037 s
% 1.88/0.80 % (4082280)Peak memory usage: 13 MB
% 1.88/0.80 % (4082280)Instructions burned: 134 (million)
% 1.88/0.80 % (4082271)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4256970153:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.88/0.80 % (4082274)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3443845854:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.88/0.80 % (4082273)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3446562705:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.88/0.80 % (4082273)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.88/0.80 % (4082283)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=1073274303:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.88/0.80 % (4082283)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.88/0.80 % (4082283)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.88/0.80 % (4082275)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1153960037:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.88/0.80 % (4082272)Instruction limit reached!
% 1.88/0.80 % (4082272)------------------------------
% 1.88/0.80 % (4082272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082272)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082272)Termination reason: Instruction limit
% 1.88/0.80 % (4082272)Termination phase: Saturation
% 1.88/0.80 % (4082272)Time elapsed: 0.092 s
% 1.88/0.80 % (4082272)Peak memory usage: 12 MB
% 1.88/0.80 % (4082272)Instructions burned: 103 (million)
% 1.88/0.80 % (4082289)ott-21_1_sil=16000:fs=off:random_seed=1798057568:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.88/0.80 % (4082273)Instruction limit reached!
% 1.88/0.80 % (4082273)------------------------------
% 1.88/0.80 % (4082273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082273)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082273)Termination reason: Instruction limit
% 1.88/0.80 % (4082273)Termination phase: Saturation
% 1.88/0.80 % (4082273)Time elapsed: 0.082 s
% 1.88/0.80 % (4082273)Peak memory usage: 13 MB
% 1.88/0.80 % (4082273)Instructions burned: 116 (million)
% 1.88/0.80 % (4082274)Instruction limit reached!
% 1.88/0.80 % (4082274)------------------------------
% 1.88/0.80 % (4082274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082274)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082274)Termination reason: Instruction limit
% 1.88/0.80 % (4082274)Termination phase: Saturation
% 1.88/0.80 % (4082274)Time elapsed: 0.149 s
% 1.88/0.80 % (4082274)Peak memory usage: 13 MB
% 1.88/0.80 % (4082274)Instructions burned: 131 (million)
% 1.88/0.80 % (4082291)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1114645237:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.88/0.80 % (4082283)Instruction limit reached!
% 1.88/0.80 % (4082283)------------------------------
% 1.88/0.80 % (4082283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082283)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082283)Termination reason: Instruction limit
% 1.88/0.80 % (4082283)Termination phase: Saturation
% 1.88/0.80 % (4082283)Time elapsed: 0.175 s
% 1.88/0.80 % (4082283)Peak memory usage: 16 MB
% 1.88/0.80 % (4082283)Instructions burned: 685 (million)
% 1.88/0.80 % (4082294)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2029317904:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 1.88/0.80 % (4082275)Instruction limit reached!
% 1.88/0.80 % (4082275)------------------------------
% 1.88/0.80 % (4082275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082275)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082275)Termination reason: Instruction limit
% 1.88/0.80 % (4082275)Termination phase: Saturation
% 1.88/0.80 % (4082275)Time elapsed: 0.188 s
% 1.88/0.80 % (4082275)Peak memory usage: 13 MB
% 1.88/0.80 % (4082275)Instructions burned: 160 (million)
% 1.88/0.80 % (4082292)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3302659396:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 1.88/0.80 % Exception at run slice level
% 1.88/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.88/0.80 % (4082296)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1245578161:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 1.88/0.80 % Exception at run slice level
% 1.88/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.88/0.80 % (4082300)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=115218195:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 1.88/0.80 % (4082300)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.88/0.80 % (4082289)Instruction limit reached!
% 1.88/0.80 % (4082289)------------------------------
% 1.88/0.80 % (4082289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082289)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082289)Termination reason: Instruction limit
% 1.88/0.80 % (4082289)Termination phase: Saturation
% 1.88/0.80 % (4082289)Time elapsed: 0.149 s
% 1.88/0.80 % (4082289)Peak memory usage: 13 MB
% 1.88/0.80 % (4082289)Instructions burned: 180 (million)
% 1.88/0.80 % (4082298)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=2281913725:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 1.88/0.80 % (4082298)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.88/0.80 % (4082303)fmb+10_1_sil=64000:random_seed=3225087060:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 1.88/0.80 % (4082303)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.88/0.80 % Exception at run slice level
% 1.88/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.88/0.80 % (4082305)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=187674654:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 1.88/0.80 % Exception at run slice level
% 1.88/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.88/0.80 % (4082307)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3542364798:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 1.88/0.80 % Exception at run slice level
% 1.88/0.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.88/0.80 % (4082309)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1388809889:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 1.88/0.80 % (4082309)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.88/0.80 % (4082270) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4082264-4082270"...
% 1.88/0.80 % (4082270)...printing done.
% 1.88/0.80 % (4082270)Refutation found. Thanks to Tanya!
% 1.88/0.80 % SZS status Theorem for theBenchmark
% 1.88/0.80 % SZS output start Proof for theBenchmark
% 1.88/0.80 thf(type_def_5, type, b: $tType).
% 1.88/0.80 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.88/0.80 thf(func_def_3, type, sK0: (((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_4, type, sK1: (((b > $o) > b) > b)).
% 1.88/0.80 thf(func_def_5, type, sK2: ((b > $o) > b)).
% 1.88/0.80 thf(func_def_6, type, sK3: (b > $o)).
% 1.88/0.80 thf(func_def_7, type, sK4: b).
% 1.88/0.80 thf(func_def_8, type, vNOT: ($o > $o)).
% 1.88/0.80 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.88/0.80 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.88/0.80 thf(func_def_13, type, db1: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_14, type, sK6: (((b > $o) > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_15, type, db2: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_16, type, db3: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_17, type, db4: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_18, type, db5: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_19, type, sK7: (((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_20, type, sK8: (((b > $o) > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_21, type, sK9: (((b > $o) > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_22, type, sK10: ((b > (b > $o) > b) > ((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_23, type, sK11: ((b > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_24, type, sK12: (((b > $o) > b > b) > ((b > $o) > b > b) > b)).
% 1.88/0.80 thf(func_def_25, type, sK13: (((b > $o) > b > b) > ((b > $o) > b > b) > b)).
% 1.88/0.80 thf(func_def_26, type, sK14: (((b > $o) > (b > $o) > (b > $o) > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_27, type, db6: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_28, type, db7: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_29, type, db8: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_30, type, db9: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_31, type, sK15: (((b > $o) > b > b) > b)).
% 1.88/0.80 thf(func_def_32, type, sK16: (((b > $o) > b) > (b > (b > $o) > (b > $o) > b) > b > b > $o)).
% 1.88/0.80 thf(func_def_33, type, sK17: (((b > $o) > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_34, type, sK18: ((b > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_35, type, sK19: (((b > $o) > b > b) > ((b > $o) > b > b) > b)).
% 1.88/0.80 thf(func_def_36, type, sK20: (((b > $o) > b > b) > ((b > $o) > b > b) > b)).
% 1.88/0.80 thf(func_def_37, type, sK21: ((b > b > $o) > b > (b > (b > $o) > b) > b)).
% 1.88/0.80 thf(func_def_38, type, sK22: (((b > $o) > b > b) > b)).
% 1.88/0.80 thf(func_def_39, type, sK23: ((b > b > $o) > (b > (b > $o) > b) > (b > (b > $o) > b) > b)).
% 1.88/0.80 thf(func_def_40, type, sK24: (((b > $o) > b > (b > $o) > b > $o) > b)).
% 1.88/0.80 thf(func_def_41, type, sK25: ((b > (b > $o) > b) > (b > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_42, type, sK26: (((b > $o) > b > (b > $o) > b > $o) > b)).
% 1.88/0.80 thf(func_def_43, type, sK27: ((b > (b > $o) > b) > (b > (b > $o) > b) > (b > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_44, type, sK28: ((b > (b > $o) > b) > (b > (b > $o) > b) > ((b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_45, type, sK29: ((b > (b > $o) > (b > $o) > b) > (b > (b > $o) > b) > ((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_46, type, sK30: (((b > $o) > b > (b > $o) > b > $o) > b > $o)).
% 1.88/0.80 thf(func_def_47, type, sK31: (((b > $o) > b > (b > $o) > b > $o) > b > $o)).
% 1.88/0.80 thf(func_def_48, type, sK32: (((b > $o) > b > b) > (b > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_49, type, sK33: (b > ((b > $o) > b > b) > b > $o)).
% 1.88/0.80 thf(func_def_50, type, sK34: (b > (b > (b > $o) > b) > ((b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_51, type, sK35: ((b > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_52, type, sK36: (((b > $o) > (b > $o) > b) > ((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_53, type, sK37: (((b > $o) > (b > $o) > (b > $o) > b) > ((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_54, type, sK38: (((b > $o) > (b > $o) > (b > $o) > b) > ((b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_55, type, sK39: (((b > $o) > (b > $o) > (b > $o) > b) > ((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_56, type, sK40: (((b > $o) > (b > $o) > (b > $o) > b) > ((b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_57, type, sK41: (((b > $o) > (b > $o) > (b > $o) > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_58, type, sK42: ((b > b > b) > (b > (b > $o) > b) > (b > b > b) > b)).
% 1.88/0.80 thf(func_def_59, type, sK43: ((b > b > b) > (b > (b > $o) > b) > (b > b > b) > b)).
% 1.88/0.80 thf(func_def_60, type, sK44: (b > (b > (b > $o) > b) > (b > b > b) > b)).
% 1.88/0.80 thf(func_def_61, type, sK45: ((b > (b > $o) > b) > b > b)).
% 1.88/0.80 thf(func_def_62, type, sK46: (b > (b > (b > $o) > b) > (b > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_63, type, sK47: (b > (b > (b > $o) > b) > (b > b > b) > b)).
% 1.88/0.80 thf(func_def_64, type, sK48: (b > (b > (b > $o) > b) > b)).
% 1.88/0.80 thf(func_def_65, type, sK49: ((b > (b > $o) > b) > (b > (b > $o) > b) > (b > (b > $o) > b) > (b > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_66, type, sK50: (b > (b > b > b) > b)).
% 1.88/0.80 thf(func_def_67, type, sK51: (b > b)).
% 1.88/0.80 thf(func_def_68, type, sK52: (b > b)).
% 1.88/0.80 thf(func_def_69, type, sK53: ((b > b > b) > b > b)).
% 1.88/0.80 thf(func_def_70, type, sK54: (b > ((b > $o) > b > b) > b > $o)).
% 1.88/0.80 thf(func_def_71, type, sK55: ((b > b > b) > (b > (b > $o) > b) > (b > b > (b > $o) > b) > b)).
% 1.88/0.80 thf(func_def_72, type, sK56: ((b > (b > $o) > b > b) > b)).
% 1.88/0.80 thf(func_def_73, type, sK57: (((b > $o) > (b > $o) > (b > $o) > (b > $o) > (b > $o) > (b > $o) > (b > $o) > b) > b > $o)).
% 1.88/0.80 thf(func_def_74, type, db10: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_75, type, db11: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_76, type, db12: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_77, type, db13: !>[X0: $tType]:(X0)).
% 1.88/0.80 thf(func_def_78, type, sK58: ((b > (b > $o) > (b > $o) > b) > (b > (b > $o) > b) > (b > (b > $o) > b) > b > b > $o)).
% 1.88/0.80 thf(func_def_79, type, sK59: (((b > $o) > b) > b > $o)).
% 1.88/0.80 thf(f1,conjecture,(
% 1.88/0.80 ! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (X1 @ X3) => (X1 @ X2)) => ? [X4 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X3 : b] : (X1 @ X3) => (X1 @ (X4 @ X1)))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (X6 @ X7) => (X6 @ (X5 @ X6)))),
% 1.88/0.80 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5310_SUB4)).
% 1.88/0.80 thf(f2,negated_conjecture,(
% 1.88/0.80 ~(! [X0 : ((b > $o) > b > $o)] : (! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (X1 @ X3) => (X1 @ X2)) => ? [X4 : ((b > $o) > b)] : ! [X1 : (b > $o)] : (? [X3 : b] : (X1 @ X3) => (X1 @ (X4 @ X1)))) => ? [X5 : ((b > $o) > b)] : ! [X6 : (b > $o)] : (? [X7 : b] : (X6 @ X7) => (X6 @ (X5 @ X6))))),
% 1.88/0.80 inference(negated_conjecture,[status(cth)],[f1])).
% 1.88/0.80 thf(f3,plain,(
% 1.88/0.80 ~((! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (X1 @ X3) => (X1 @ X2)) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : (? [X6 : b] : (X5 @ X6) => (X5 @ (X4 @ X5)))) => ? [X7 : ((b > $o) > b)] : ! [X8 : (b > $o)] : (? [X9 : b] : (X8 @ X9) => (X8 @ (X7 @ X8))))),
% 1.88/0.80 inference(rectify,[],[f2])).
% 1.88/0.80 thf(f4,plain,(
% 1.88/0.80 ~((! [X1 : (b > $o)] : ? [X2 : b] : (? [X3 : b] : (((X1 @ X3)) = $true) => (((X1 @ X2)) = $true)) => ? [X4 : ((b > $o) > b)] : ! [X5 : (b > $o)] : (? [X6 : b] : (((X5 @ X6)) = $true) => (((X5 @ (X4 @ X5))) = $true))) => ? [X7 : ((b > $o) > b)] : ! [X8 : (b > $o)] : (? [X9 : b] : (((X8 @ X9)) = $true) => (((X8 @ (X7 @ X8))) = $true)))),
% 1.88/0.80 inference(fool_elimination,[],[f3])).
% 1.88/0.80 thf(f5,plain,(
% 1.88/0.80 ~((! [X0 : (b > $o)] : ? [X1 : b] : (? [X2 : b] : ($true = ((X0 @ X2))) => ($true = ((X0 @ X1)))) => ? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (? [X5 : b] : ($true = ((X4 @ X5))) => ($true = ((X4 @ (X3 @ X4)))))) => ? [X6 : ((b > $o) > b)] : ! [X7 : (b > $o)] : (? [X8 : b] : ($true = ((X7 @ X8))) => ($true = ((X7 @ (X6 @ X7))))))),
% 1.88/0.80 inference(rectify,[],[f4])).
% 1.88/0.80 thf(f6,plain,(
% 1.88/0.80 ! [X6 : ((b > $o) > b)] : ? [X7 : (b > $o)] : (($true != ((X7 @ (X6 @ X7)))) & ? [X8 : b] : ($true = ((X7 @ X8)))) & (? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (($true = ((X4 @ (X3 @ X4)))) | ! [X5 : b] : ($true != ((X4 @ X5)))) | ? [X0 : (b > $o)] : ! [X1 : b] : (($true != ((X0 @ X1))) & ? [X2 : b] : ($true = ((X0 @ X2)))))),
% 1.88/0.80 inference(ennf_transformation,[],[f5])).
% 1.88/0.80 thf(f7,plain,(
% 1.88/0.80 ! [X0 : ((b > $o) > b)] : ? [X1 : (b > $o)] : (($true != ((X1 @ (X0 @ X1)))) & ? [X2 : b] : (((X1 @ X2)) = $true)) & (? [X3 : ((b > $o) > b)] : ! [X4 : (b > $o)] : (($true = ((X4 @ (X3 @ X4)))) | ! [X5 : b] : ($true != ((X4 @ X5)))) | ? [X6 : (b > $o)] : ! [X7 : b] : ((((X6 @ X7)) != $true) & ? [X8 : b] : ($true = ((X6 @ X8)))))),
% 1.88/0.80 inference(rectify,[],[f6])).
% 1.88/0.80 thf(f8,plain,(
% 1.88/0.80 ! [X0 : ((b > $o) > b)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0))))) & ($true = ((sK0 @ X0 @ (sK1 @ X0))))) & (! [X4 : (b > $o)] : (($true = ((X4 @ (sK2 @ X4)))) | ! [X5 : b] : ($true != ((X4 @ X5)))) | ! [X7 : b] : (($true != ((sK3 @ X7))) & ($true = ((sK3 @ sK4)))))),
% 1.88/0.80 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0),skolemize(X3,sK2),skolemize(X6,sK3),skolemize(X8,sK4)],[f7])).
% 1.88/0.80 thf(f9,plain,(
% 1.88/0.80 ( ! [X4 : (b > $o),X5 : b] : (($true = ((X4 @ (sK2 @ X4)))) | ($true != ((X4 @ X5))) | ($true = ((sK3 @ sK4)))) )),
% 1.88/0.80 inference(cnf_transformation,[],[f8])).
% 1.88/0.80 thf(f10,plain,(
% 1.88/0.80 ( ! [X7 : b,X4 : (b > $o),X5 : b] : (($true = ((X4 @ (sK2 @ X4)))) | ($true != ((X4 @ X5))) | ($true != ((sK3 @ X7)))) )),
% 1.88/0.80 inference(cnf_transformation,[],[f8])).
% 1.88/0.80 thf(f11,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b)] : (($true = ((sK0 @ X0 @ (sK1 @ X0))))) )),
% 1.88/0.80 inference(cnf_transformation,[],[f8])).
% 1.88/0.80 thf(f12,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b)] : (($true != ((sK0 @ X0 @ (X0 @ (sK0 @ X0)))))) )),
% 1.88/0.80 inference(cnf_transformation,[],[f8])).
% 1.88/0.80 thf(f16,definition,(
% 1.88/0.80 spl5_1 <=> ($true = ((sK3 @ sK4)))),
% 1.88/0.80 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 1.88/0.80 thf(f18,plain,(
% 1.88/0.80 ($true = ((sK3 @ sK4))) | ~spl5_1),
% 1.88/0.80 inference(avatar_component_clause,[],[f16])).
% 1.88/0.80 thf(f20,definition,(
% 1.88/0.80 spl5_2 <=> ! [X4 : (b > $o),X5 : b] : (($true = ((X4 @ (sK2 @ X4)))) | ($true != ((X4 @ X5))))),
% 1.88/0.80 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 1.88/0.80 thf(f21,plain,(
% 1.88/0.80 ( ! [X4 : (b > $o),X5 : b] : (($true != ((X4 @ X5))) | ($true = ((X4 @ (sK2 @ X4))))) ) | ~spl5_2),
% 1.88/0.80 inference(avatar_component_clause,[],[f20])).
% 1.88/0.80 thf(f22,plain,(
% 1.88/0.80 spl5_1 | spl5_2),
% 1.88/0.80 inference(avatar_split_clause,[],[f9,f20,f16])).
% 1.88/0.80 thf(f24,definition,(
% 1.88/0.80 spl5_3 <=> ! [X7 : b] : ($true != ((sK3 @ X7)))),
% 1.88/0.80 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 1.88/0.80 thf(f25,plain,(
% 1.88/0.80 ( ! [X7 : b] : (($true != ((sK3 @ X7)))) ) | ~spl5_3),
% 1.88/0.80 inference(avatar_component_clause,[],[f24])).
% 1.88/0.80 thf(f26,plain,(
% 1.88/0.80 spl5_3 | spl5_2),
% 1.88/0.80 inference(avatar_split_clause,[],[f10,f20,f24])).
% 1.88/0.80 thf(f38,plain,(
% 1.88/0.80 ( ! [X2 : ((b > $o) > b),X0 : (b > (b > $o) > b),X1 : b] : (($true != $true) | ($true = (((^[Y0 : b]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : b]: (Y1)) @ Y0))) @ (sK2 @ (^[Y0 : b]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : b]: (Y1)) @ Y0))))))) | (((X0 @ X1)) != X2) | (((sK1 @ X2)) != X1)) ) | ~spl5_2),
% 1.88/0.80 inference(constrained_superposition,[],[f21,f11])).
% 1.88/0.80 thf(f42,plain,(
% 1.88/0.80 ( ! [X2 : ((b > $o) > b),X0 : (b > (b > $o) > b),X1 : b] : (($true = (((^[Y0 : b]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : b]: (Y1)) @ Y0))) @ (sK2 @ (^[Y0 : b]: (sK0 @ (X0 @ Y0) @ ((^[Y1 : b]: (Y1)) @ Y0))))))) | (((X0 @ X1)) != X2) | (((sK1 @ X2)) != X1)) ) | ~spl5_2),
% 1.88/0.80 inference(trivial_inequality_removal,[],[f38])).
% 1.88/0.80 thf(f43,plain,(
% 1.88/0.80 ( ! [X2 : ((b > $o) > b),X0 : (b > (b > $o) > b),X1 : b] : ((((sK1 @ X2)) != X1) | ($true = ((sK0 @ (X0 @ (sK2 @ (^[Y0 : b]: (sK0 @ (X0 @ Y0) @ Y0)))) @ (sK2 @ (^[Y0 : b]: (sK0 @ (X0 @ Y0) @ Y0)))))) | (((X0 @ X1)) != X2)) ) | ~spl5_2),
% 1.88/0.80 inference(beta-eta_normalization,[],[f42])).
% 1.88/0.80 thf(f313,plain,(
% 1.88/0.80 ( ! [X0 : (b > (b > $o) > b),X1 : ((b > $o) > b)] : (($true = ((sK0 @ (X0 @ (sK2 @ (^[Y0 : b]: (sK0 @ (X0 @ Y0) @ Y0)))) @ (sK2 @ (^[Y0 : b]: (sK0 @ (X0 @ Y0) @ Y0)))))) | (((X0 @ (sK1 @ X1))) != X1)) ) | ~spl5_2),
% 1.88/0.80 inference(equality_resolution,[],[f43])).
% 1.88/0.80 thf(f462,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b),X1 : (b > (b > $o) > b > b)] : (($true != $true) | ((((^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ ((^[Y2 : b]: ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y3 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1))))) @ (sK1 @ X0))) != X0) | ((^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ ((^[Y2 : b]: ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y3 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1))))) != (^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ (X1 @ (sK2 @ (^[Y3 : b]: (sK0 @ (^[Y4 : b > $o]: (sK2 @ (^[Y5 : b]: (Y4 @ (X1 @ Y3 @ Y4 @ Y5))))) @ Y3))) @ Y1 @ Y2)))))))) | ((^[Y0 : b]: (Y0)) != ((X1 @ (sK2 @ (^[Y0 : b]: (sK0 @ (^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ (X1 @ Y0 @ Y1 @ Y2))))) @ Y0))) @ (sK0 @ (^[Y0 : b > $o]: (sK2 @ (^[Y1 : b]: (Y0 @ (X1 @ (sK2 @ (^[Y2 : b]: (sK0 @ (^[Y3 : b > $o]: (sK2 @ (^[Y4 : b]: (Y3 @ (X1 @ Y2 @ Y3 @ Y4))))) @ Y2))) @ Y0 @ Y1)))))))))) ) | ~spl5_2),
% 1.88/0.80 inference(constrained_superposition,[],[f12,f313])).
% 1.88/0.80 thf(f466,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b),X1 : (b > (b > $o) > b > b)] : (((((^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ ((^[Y2 : b]: ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y3 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1))))) @ (sK1 @ X0))) != X0) | ((^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ ((^[Y2 : b]: ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y3 @ (X1 @ Y2 @ Y3 @ Y4))))))) @ Y0 @ Y1))))) != (^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ (X1 @ (sK2 @ (^[Y3 : b]: (sK0 @ (^[Y4 : b > $o]: (sK2 @ (^[Y5 : b]: (Y4 @ (X1 @ Y3 @ Y4 @ Y5))))) @ Y3))) @ Y1 @ Y2)))))))) | ((^[Y0 : b]: (Y0)) != ((X1 @ (sK2 @ (^[Y0 : b]: (sK0 @ (^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ (X1 @ Y0 @ Y1 @ Y2))))) @ Y0))) @ (sK0 @ (^[Y0 : b > $o]: (sK2 @ (^[Y1 : b]: (Y0 @ (X1 @ (sK2 @ (^[Y2 : b]: (sK0 @ (^[Y3 : b > $o]: (sK2 @ (^[Y4 : b]: (Y3 @ (X1 @ Y2 @ Y3 @ Y4))))) @ Y2))) @ Y0 @ Y1)))))))))) ) | ~spl5_2),
% 1.88/0.80 inference(trivial_inequality_removal,[],[f462])).
% 1.88/0.80 thf(f467,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b),X1 : (b > (b > $o) > b > b)] : (((^[Y0 : b]: (Y0)) != ((X1 @ (sK2 @ (^[Y0 : b]: (sK0 @ (^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ (X1 @ Y0 @ Y1 @ Y2))))) @ Y0))) @ (sK0 @ (^[Y0 : b > $o]: (sK2 @ (^[Y1 : b]: (Y0 @ (X1 @ (sK2 @ (^[Y2 : b]: (sK0 @ (^[Y3 : b > $o]: (sK2 @ (^[Y4 : b]: (Y3 @ (X1 @ Y2 @ Y3 @ Y4))))) @ Y2))) @ Y0 @ Y1))))))))) | ((^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ (X1 @ (sK2 @ (^[Y3 : b]: (sK0 @ (^[Y4 : b > $o]: (sK2 @ (^[Y5 : b]: (Y4 @ (X1 @ Y3 @ Y4 @ Y5))))) @ Y3))) @ Y1 @ Y2))))))) != (^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ (X1 @ Y0 @ Y1 @ Y2)))))))) | ((^[Y0 : b > $o]: (sK2 @ (^[Y1 : b]: (Y0 @ (X1 @ (sK1 @ X0) @ Y0 @ Y1))))) != X0)) ) | ~spl5_2),
% 1.88/0.80 inference(beta-eta_normalization,[],[f466])).
% 1.88/0.80 thf(f3135,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b)] : (((^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ ((^[Y3 : b]: ((^[Y4 : b > $o]: ((^[Y5 : b]: (Y5)))))) @ (sK2 @ (^[Y3 : b]: (sK0 @ (^[Y4 : b > $o]: (sK2 @ (^[Y5 : b]: (Y4 @ ((^[Y6 : b]: ((^[Y7 : b > $o]: ((^[Y8 : b]: (Y8)))))) @ Y3 @ Y4 @ Y5))))) @ Y3))) @ Y1 @ Y2))))))) != (^[Y0 : b]: ((^[Y1 : b > $o]: (sK2 @ (^[Y2 : b]: (Y1 @ ((^[Y3 : b]: ((^[Y4 : b > $o]: ((^[Y5 : b]: (Y5)))))) @ Y0 @ Y1 @ Y2)))))))) | ((^[Y0 : b > $o]: (sK2 @ (^[Y1 : b]: (Y0 @ ((^[Y2 : b]: ((^[Y3 : b > $o]: ((^[Y4 : b]: (Y4)))))) @ (sK1 @ X0) @ Y0 @ Y1))))) != X0)) ) | ~spl5_2),
% 1.88/0.80 inference(equality_resolution,[],[f467])).
% 1.88/0.80 thf(f3136,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b)] : (((^[Y0 : b]: (sK2)) != (^[Y0 : b]: (sK2))) | (sK2 != X0)) ) | ~spl5_2),
% 1.88/0.80 inference(beta-eta_normalization,[],[f3135])).
% 1.88/0.80 thf(f3137,plain,(
% 1.88/0.80 ( ! [X0 : ((b > $o) > b)] : ((sK2 != X0)) ) | ~spl5_2),
% 1.88/0.80 inference(trivial_inequality_removal,[],[f3136])).
% 1.88/0.80 thf(f3152,plain,(
% 1.88/0.80 $false | ~spl5_2),
% 1.88/0.80 inference(equality_resolution,[],[f3137])).
% 1.88/0.80 thf(f3153,plain,(
% 1.88/0.80 ~spl5_2),
% 1.88/0.80 inference(avatar_contradiction_clause,[],[f3152])).
% 1.88/0.80 thf(f3154,plain,(
% 1.88/0.80 $false | (~spl5_1 | ~spl5_3)),
% 1.88/0.80 inference(backward_subsumption_resolution,[],[f18,f25])).
% 1.88/0.80 thf(f3157,plain,(
% 1.88/0.80 ~spl5_1 | ~spl5_3),
% 1.88/0.80 inference(avatar_contradiction_clause,[],[f3154])).
% 1.88/0.80 cnf(s1, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f22])).
% 1.88/0.80 cnf(s2, plain, spl5_2 | spl5_3, inference(sat_conversion,[],[f26])).
% 1.88/0.80 cnf(s3, plain, ~spl5_2, inference(sat_conversion,[],[f3153])).
% 1.88/0.80 cnf(s4, plain, ~spl5_1 | ~spl5_3, inference(sat_conversion,[],[f3157])).
% 1.88/0.80 cnf(s5, plain, spl5_3, inference(rat,[],[s2,s3])).
% 1.88/0.80 cnf(s6, plain, ~spl5_1, inference(rat,[],[s4,s5])).
% 1.88/0.80 cnf(s7, plain, $false, inference(rat,[],[s1,s3,s6])).
% 1.88/0.80 thf(f3158,plain,(
% 1.88/0.80 $false),
% 1.88/0.80 inference(avatar_sat_refutation,[],[s7])).
% 1.88/0.80 % SZS output end Proof for theBenchmark
% 1.88/0.80 % (4082270)------------------------------
% 1.88/0.80 % (4082270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.88/0.80 % (4082270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.88/0.80 % (4082270)CaDiCaL version: 2.1.3
% 1.88/0.80 % (4082270)Termination reason: Refutation
% 1.88/0.80 % (4082270)Time elapsed: 0.522 s
% 1.88/0.80 % (4082270)Peak memory usage: 16 MB
% 1.88/0.80 % (4082270)Instructions burned: 1016 (million)
% 1.88/0.80 % (4082264)Success in time 0.571 s
% 1.88/0.80 % Vampire exiting
%------------------------------------------------------------------------------