%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT165+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Tue Sep 29 12:37:03 PM UTC 2026
% Result : ContradictoryAxioms 5.68s 1.43s
% Output : Refutation 5.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-5 aty)
% Number of variables : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f375,axiom,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(f525,axiom,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f527,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(c_COMBB(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(f529,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(c_COMBS(X5,X4,X3,X2,X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(f1939,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f375]) ).
fof(f2144,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f525]) ).
fof(f2146,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(c_COMBB(X5,X4,X3,X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
inference(cnf_transformation,[],[f527]) ).
fof(f2148,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_COMBS(X5,X4,X3,X2,X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
inference(cnf_transformation,[],[f529]) ).
fof(f2451,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(X0,hAPP(X1,hAPP(X2,X1))) = hAPP(c_COMBS(X3,X4,X5,c_COMBB(X6,X7,X8,X0),X2),X1),
inference(superposition,[],[f2148,f2146]) ).
fof(f2478,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X7,hAPP(X6,X7)) != hAPP(c_COMBS(X0,X1,X2,c_COMBB(X3,X4,X5,c_Nat_OSuc),X6),X7),
inference(superposition,[],[f1939,f2451]) ).
fof(f2487,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X0,X0) != hAPP(c_COMBS(X2,X3,X4,c_COMBB(X5,X6,X7,c_Nat_OSuc),c_COMBI(X1)),X0),
inference(superposition,[],[f2478,f2144]) ).
fof(f2503,plain,
$false,
inference(equality_resolution,[],[f2487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SCT165+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 23:51:34 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 Running first-order theorem proving
% 0.08/0.34 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.68/1.43 % (2880826)Detected formulas, will run a generic FOF schedule.
% 5.68/1.43 % (2880831)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3553338214:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.68/1.43 % (2880832)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1855257060:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.68/1.43 % (2880835)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3676410806:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.68/1.43 % (2880837)dis-21_1_sil=8000:lcm=predicate:random_seed=1757345427:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 5.68/1.43 % (2880834)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3418428993:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.68/1.43 % (2880833)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3150157226:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.68/1.43 % (2880836)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=43728396:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.68/1.43 % (2880834)Instruction limit reached!
% 5.68/1.43 % (2880834)------------------------------
% 5.68/1.43 % (2880834)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880834)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880834)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880834)Termination reason: Instruction limit
% 5.68/1.43 % (2880834)Termination phase: Saturation
% 5.68/1.43 % (2880834)Time elapsed: 0.027 s
% 5.68/1.43 % (2880834)Peak memory usage: 89 MB
% 5.68/1.43 % (2880834)Instructions burned: 111 (million)
% 5.68/1.43 % (2880837)Instruction limit reached!
% 5.68/1.43 % (2880837)------------------------------
% 5.68/1.43 % (2880837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880837)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880837)Termination reason: Instruction limit
% 5.68/1.43 % (2880837)Termination phase: Saturation
% 5.68/1.43 % (2880837)Time elapsed: 0.034 s
% 5.68/1.43 % (2880837)Peak memory usage: 89 MB
% 5.68/1.43 % (2880837)Instructions burned: 131 (million)
% 5.68/1.43 % (2880835)Instruction limit reached!
% 5.68/1.43 % (2880835)------------------------------
% 5.68/1.43 % (2880835)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880835)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880835)Termination reason: Instruction limit
% 5.68/1.43 % (2880835)Termination phase: Saturation
% 5.68/1.43 % (2880835)Time elapsed: 0.036 s
% 5.68/1.43 % (2880835)Peak memory usage: 89 MB
% 5.68/1.43 % (2880835)Instructions burned: 119 (million)
% 5.68/1.43 % (2880836)Instruction limit reached!
% 5.68/1.43 % (2880836)------------------------------
% 5.68/1.43 % (2880836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880836)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880836)Termination reason: Instruction limit
% 5.68/1.43 % (2880836)Termination phase: Saturation
% 5.68/1.43 % (2880836)Time elapsed: 0.054 s
% 5.68/1.43 % (2880836)Peak memory usage: 90 MB
% 5.68/1.43 % (2880836)Instructions burned: 139 (million)
% 5.68/1.43 % (2880845)lrs+10_1_sil=8000:sp=occurrence:random_seed=1389085266:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.68/1.43 % (2880847)lrs+1011_1_sil=32000:sp=occurrence:random_seed=549432770:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 5.68/1.43 % (2880846)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3613937818:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 5.68/1.43 % (2880848)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1400385489:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.68/1.43 % (2880846)Instruction limit reached!
% 5.68/1.43 % (2880846)------------------------------
% 5.68/1.43 % (2880846)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880846)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880846)Termination reason: Instruction limit
% 5.68/1.43 % (2880846)Termination phase: Saturation
% 5.68/1.43 % (2880846)Time elapsed: 0.045 s
% 5.68/1.43 % (2880846)Peak memory usage: 90 MB
% 5.68/1.43 % (2880846)Instructions burned: 157 (million)
% 5.68/1.43 % (2880845)Instruction limit reached!
% 5.68/1.43 % (2880845)------------------------------
% 5.68/1.43 % (2880845)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880845)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880845)Termination reason: Instruction limit
% 5.68/1.43 % (2880845)Termination phase: Saturation
% 5.68/1.43 % (2880845)Time elapsed: 0.094 s
% 5.68/1.43 % (2880845)Peak memory usage: 91 MB
% 5.68/1.43 % (2880845)Instructions burned: 285 (million)
% 5.68/1.43 % (2880848)Instruction limit reached!
% 5.68/1.43 % (2880848)------------------------------
% 5.68/1.43 % (2880848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880848)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880848)Termination reason: Instruction limit
% 5.68/1.43 % (2880848)Termination phase: Saturation
% 5.68/1.43 % (2880848)Time elapsed: 0.074 s
% 5.68/1.43 % (2880848)Peak memory usage: 91 MB
% 5.68/1.43 % (2880848)Instructions burned: 249 (million)
% 5.68/1.43 % (2880847)Instruction limit reached!
% 5.68/1.43 % (2880847)------------------------------
% 5.68/1.43 % (2880847)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880847)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880847)Termination reason: Instruction limit
% 5.68/1.43 % (2880847)Termination phase: Saturation
% 5.68/1.43 % (2880847)Time elapsed: 0.105 s
% 5.68/1.43 % (2880847)Peak memory usage: 91 MB
% 5.68/1.43 % (2880847)Instructions burned: 327 (million)
% 5.68/1.43 % (2880853)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=159311662:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 5.68/1.43 % (2880854)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=351116419:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 5.68/1.43 % (2880855)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2786535426:cts=off:i=113:fsr=off:ss=included:sgt=4_2996 on theBenchmark for (2996ds/113Mi)
% 5.68/1.43 % (2880856)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=858639453:i=127:av=off:fsr=off:sup=off_2995 on theBenchmark for (2995ds/127Mi)
% 5.68/1.43 % (2880853)Instruction limit reached!
% 5.68/1.43 % (2880853)------------------------------
% 5.68/1.43 % (2880853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880853)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880853)Termination reason: Instruction limit
% 5.68/1.43 % (2880853)Termination phase: Saturation
% 5.68/1.43 % (2880853)Time elapsed: 0.082 s
% 5.68/1.43 % (2880853)Peak memory usage: 90 MB
% 5.68/1.43 % (2880853)Instructions burned: 296 (million)
% 5.68/1.43 % (2880855)Instruction limit reached!
% 5.68/1.43 % (2880855)------------------------------
% 5.68/1.43 % (2880855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880855)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880855)Termination reason: Instruction limit
% 5.68/1.43 % (2880855)Termination phase: Saturation
% 5.68/1.43 % (2880855)Time elapsed: 0.032 s
% 5.68/1.43 % (2880855)Peak memory usage: 90 MB
% 5.68/1.43 % (2880855)Instructions burned: 116 (million)
% 5.68/1.43 % (2880856)Instruction limit reached!
% 5.68/1.43 % (2880856)------------------------------
% 5.68/1.43 % (2880856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880856)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880856)Termination reason: Instruction limit
% 5.68/1.43 % (2880856)Termination phase: Saturation
% 5.68/1.43 % (2880856)Time elapsed: 0.030 s
% 5.68/1.43 % (2880856)Peak memory usage: 89 MB
% 5.68/1.43 % (2880856)Instructions burned: 130 (million)
% 5.68/1.43 % (2880832)First to succeed.
% 5.68/1.43 % (2880832)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2880826"
% 5.68/1.43 % (2880831)Also succeeded, but the first one will report.
% 5.68/1.43 % (2880861)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1687576646:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 5.68/1.43 % (2880861)Instruction limit reached!
% 5.68/1.43 % (2880861)------------------------------
% 5.68/1.43 % (2880861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880861)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880861)Termination reason: Instruction limit
% 5.68/1.43 % (2880861)Termination phase: Property scanning
% 5.68/1.43 % (2880861)Time elapsed: 0.022 s
% 5.68/1.43 % (2880861)Peak memory usage: 86 MB
% 5.68/1.43 % (2880861)Instructions burned: 114 (million)
% 5.68/1.43 % (2880862)lrs+10_1_sil=8000:sp=occurrence:random_seed=28804336:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2994 on theBenchmark for (2994ds/907Mi)
% 5.68/1.43 % (2880863)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3273997077:i=437:sd=1:aac=none:ss=included_2994 on theBenchmark for (2994ds/437Mi)
% 5.68/1.43 % (2880832)Refutation found. Thanks to Tanya!
% 5.68/1.43 % SZS status ContradictoryAxioms for theBenchmark
% 5.68/1.43 % SZS output start Proof for theBenchmark
% See solution above
% 5.68/1.43 % (2880832)------------------------------
% 5.68/1.43 % (2880832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.68/1.43 % (2880832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.68/1.43 % (2880832)CaDiCaL version: 2.1.3
% 5.68/1.43 % (2880832)Termination reason: Refutation
% 5.68/1.43 % (2880832)Time elapsed: 0.470 s
% 5.68/1.43 % (2880832)Peak memory usage: 136 MB
% 5.68/1.43 % (2880832)Instructions burned: 1367 (million)
% 5.68/1.43 % (2880832)------------------------------
% 5.68/1.43 % (2880832)------------------------------
% 5.68/1.43 % (2880826)Success in time 0.792 s
% 5.68/1.43 % Vampire exiting
%------------------------------------------------------------------------------