%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT132+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 : n002.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 12:36:59 PM UTC 2026
% Result : ContradictoryAxioms 6.01s 1.85s
% Output : Refutation 6.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 28 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 117 ( 117 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f511,axiom,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f513,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(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(f515,axiom,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(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(f519,axiom,
! [X0] :
( ~ hBOOL(hAPP(c_fNot,X0))
| ~ hBOOL(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(f520,axiom,
! [X0] :
( hBOOL(X0)
| hBOOL(hAPP(c_fNot,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(f2023,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f511]) ).
fof(f2025,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBB(X5,X4,X3),X2),X1),X0) = hAPP(X2,hAPP(X1,X0)),
inference(cnf_transformation,[],[f513]) ).
fof(f2027,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X5,X4,X3),X2),X1),X0) = hAPP(hAPP(X2,X0),hAPP(X1,X0)),
inference(cnf_transformation,[],[f515]) ).
fof(f2031,plain,
! [X0] :
( ~ hBOOL(hAPP(c_fNot,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f519]) ).
fof(f2032,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f520]) ).
fof(f2329,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),X4),c_COMBI(X5)),X0) = hAPP(hAPP(X4,X0),X0),
inference(superposition,[],[f2027,f2023]) ).
fof(f2348,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X1,X2,X3),c_COMBI(X4)),c_COMBI(X5)),X0) = hAPP(X0,X0),
inference(superposition,[],[f2329,f2023]) ).
fof(f2361,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),hAPP(c_COMBB(X3,X4,X5),X6)),c_COMBI(X7)),X8) = hAPP(X6,hAPP(X8,X8)),
inference(superposition,[],[f2025,f2329]) ).
fof(f2461,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),hAPP(c_COMBB(X3,X4,X5),c_fNot)),c_COMBI(X6)),X7))
| ~ hBOOL(hAPP(X7,X7)) ),
inference(superposition,[],[f2031,f2361]) ).
fof(f2462,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),hAPP(c_COMBB(X3,X4,X5),c_fNot)),c_COMBI(X6)),X7))
| hBOOL(hAPP(X7,X7)) ),
inference(superposition,[],[f2032,f2361]) ).
fof(f2493,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBI(X3)),c_COMBI(X4)),hAPP(hAPP(c_COMBS(X5,X6,X7),hAPP(c_COMBB(X8,X9,X10),c_fNot)),c_COMBI(X11))))
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBI(X3)),c_COMBI(X4)),hAPP(hAPP(c_COMBS(X5,X6,X7),hAPP(c_COMBB(X8,X9,X10),c_fNot)),c_COMBI(X11)))) ),
inference(superposition,[],[f2461,f2348]) ).
fof(f2495,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] : ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBI(X3)),c_COMBI(X4)),hAPP(hAPP(c_COMBS(X5,X6,X7),hAPP(c_COMBB(X8,X9,X10),c_fNot)),c_COMBI(X11)))),
inference(duplicate_literal_removal,[],[f2493]) ).
fof(f2509,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBI(X3)),c_COMBI(X4)),hAPP(hAPP(c_COMBS(X5,X6,X7),hAPP(c_COMBB(X8,X9,X10),c_fNot)),c_COMBI(X11))))
| hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBI(X3)),c_COMBI(X4)),hAPP(hAPP(c_COMBS(X5,X6,X7),hAPP(c_COMBB(X8,X9,X10),c_fNot)),c_COMBI(X11)))) ),
inference(superposition,[],[f2462,f2348]) ).
fof(f2516,plain,
! [X2,X3,X10,X0,X11,X1,X8,X6,X9,X7,X4,X5] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X0,X1,X2),c_COMBI(X3)),c_COMBI(X4)),hAPP(hAPP(c_COMBS(X5,X6,X7),hAPP(c_COMBB(X8,X9,X10),c_fNot)),c_COMBI(X11)))),
inference(duplicate_literal_removal,[],[f2509]) ).
fof(f2518,plain,
$false,
inference(forward_subsumption_resolution,[],[f2516,f2495]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT132+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n002.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Sun Sep 27 23:49:52 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 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
% 6.01/1.85 % (4013768)Detected formulas, will run a generic FOF schedule.
% 6.01/1.85 % (4013773)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=3866197053:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.01/1.85 % (4013779)dis-21_1_sil=8000:lcm=predicate:random_seed=1140590176: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)
% 6.01/1.85 % (4013777)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2871510464:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.01/1.85 % (4013775)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=2202092401:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.01/1.85 % (4013776)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3940555016:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.01/1.85 % (4013774)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=2363106821:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.01/1.85 % (4013776)Refutation not found, incomplete strategy
% 6.01/1.85 % (4013776)------------------------------
% 6.01/1.85 % (4013776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013776)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013776)Termination reason: Refutation not found, incomplete strategy
% 6.01/1.85 % (4013776)Time elapsed: 0.004 s
% 6.01/1.85 % (4013776)Peak memory usage: 89 MB
% 6.01/1.85 % (4013776)Instructions burned: 5 (million)
% 6.01/1.85 % (4013778)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3167295484:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.01/1.85 % (4013779)Instruction limit reached!
% 6.01/1.85 % (4013779)------------------------------
% 6.01/1.85 % (4013779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013779)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013779)Termination reason: Instruction limit
% 6.01/1.85 % (4013779)Termination phase: Saturation
% 6.01/1.85 % (4013779)Time elapsed: 0.066 s
% 6.01/1.85 % (4013779)Peak memory usage: 90 MB
% 6.01/1.85 % (4013779)Instructions burned: 130 (million)
% 6.01/1.85 % (4013777)Instruction limit reached!
% 6.01/1.85 % (4013777)------------------------------
% 6.01/1.85 % (4013777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013777)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013777)Termination reason: Instruction limit
% 6.01/1.85 % (4013777)Termination phase: Saturation
% 6.01/1.85 % (4013777)Time elapsed: 0.074 s
% 6.01/1.85 % (4013777)Peak memory usage: 89 MB
% 6.01/1.85 % (4013777)Instructions burned: 119 (million)
% 6.01/1.85 % (4013778)Instruction limit reached!
% 6.01/1.85 % (4013778)------------------------------
% 6.01/1.85 % (4013778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013778)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013778)Termination reason: Instruction limit
% 6.01/1.85 % (4013778)Termination phase: Saturation
% 6.01/1.85 % (4013778)Time elapsed: 0.079 s
% 6.01/1.85 % (4013778)Peak memory usage: 90 MB
% 6.01/1.85 % (4013778)Instructions burned: 140 (million)
% 6.01/1.85 % (4013787)lrs+10_1_sil=8000:sp=occurrence:random_seed=2281961872:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.01/1.85 % (4013788)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2395806359:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.01/1.85 % (4013789)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1903438475:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.01/1.85 % (4013776)------------------------------
% 6.01/1.85 % (4013776)------------------------------
% 6.01/1.85 % (4013788)Instruction limit reached!
% 6.01/1.85 % (4013788)------------------------------
% 6.01/1.85 % (4013788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013788)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013788)Termination reason: Instruction limit
% 6.01/1.85 % (4013788)Termination phase: Saturation
% 6.01/1.85 % (4013788)Time elapsed: 0.090 s
% 6.01/1.85 % (4013788)Peak memory usage: 90 MB
% 6.01/1.85 % (4013788)Instructions burned: 157 (million)
% 6.01/1.85 % (4013787)Instruction limit reached!
% 6.01/1.85 % (4013787)------------------------------
% 6.01/1.85 % (4013787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013787)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013787)Termination reason: Instruction limit
% 6.01/1.85 % (4013787)Termination phase: Saturation
% 6.01/1.85 % (4013787)Time elapsed: 0.182 s
% 6.01/1.85 % (4013787)Peak memory usage: 92 MB
% 6.01/1.85 % (4013787)Instructions burned: 285 (million)
% 6.01/1.85 % (4013793)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=511041828:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 6.01/1.85 % (4013789)Instruction limit reached!
% 6.01/1.85 % (4013789)------------------------------
% 6.01/1.85 % (4013789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013789)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013789)Termination reason: Instruction limit
% 6.01/1.85 % (4013789)Termination phase: Saturation
% 6.01/1.85 % (4013789)Time elapsed: 0.189 s
% 6.01/1.85 % (4013789)Peak memory usage: 91 MB
% 6.01/1.85 % (4013789)Instructions burned: 326 (million)
% 6.01/1.85 % (4013794)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=992161475:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.01/1.85 % (4013773)First to succeed.
% 6.01/1.85 % (4013773)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4013768"
% 6.01/1.85 % (4013795)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=337344567:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.01/1.85 % (4013793)Instruction limit reached!
% 6.01/1.85 % (4013793)------------------------------
% 6.01/1.85 % (4013793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013793)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013793)Termination reason: Instruction limit
% 6.01/1.85 % (4013793)Termination phase: Saturation
% 6.01/1.85 % (4013793)Time elapsed: 0.136 s
% 6.01/1.85 % (4013793)Peak memory usage: 92 MB
% 6.01/1.85 % (4013793)Instructions burned: 249 (million)
% 6.01/1.85 % (4013798)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=571963067:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 6.01/1.85 % (4013794)Instruction limit reached!
% 6.01/1.85 % (4013794)------------------------------
% 6.01/1.85 % (4013794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013794)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013794)Termination reason: Instruction limit
% 6.01/1.85 % (4013794)Termination phase: Saturation
% 6.01/1.85 % (4013794)Time elapsed: 0.159 s
% 6.01/1.85 % (4013794)Peak memory usage: 90 MB
% 6.01/1.85 % (4013794)Instructions burned: 294 (million)
% 6.01/1.85 % (4013773)Refutation found. Thanks to Tanya!
% 6.01/1.85 % SZS status ContradictoryAxioms for theBenchmark
% 6.01/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 6.01/1.85 % (4013773)------------------------------
% 6.01/1.85 % (4013773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.01/1.85 % (4013773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.01/1.85 % (4013773)CaDiCaL version: 2.1.3
% 6.01/1.85 % (4013773)Termination reason: Refutation
% 6.01/1.85 % (4013773)Time elapsed: 0.496 s
% 6.01/1.85 % (4013773)Peak memory usage: 144 MB
% 6.01/1.85 % (4013773)Instructions burned: 1463 (million)
% 6.01/1.85 % (4013773)------------------------------
% 6.01/1.85 % (4013773)------------------------------
% 6.01/1.85 % (4013768)Success in time 0.795 s
% 6.01/1.85 % Vampire exiting
%------------------------------------------------------------------------------