%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG077+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:35:25 PM UTC 2026
% Result : Theorem 5.31s 1.68s
% Output : Refutation 5.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 90 ( 29 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 108 ( 52 ~; 38 |; 16 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X0)
& aScalar0(X1) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aScalar0(X0)
& aScalar0(X1)
& aScalar0(X2) )
=> ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(f48,axiom,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(f51,axiom,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(f53,axiom,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(f55,axiom,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(f59,conjecture,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f60,negated_conjecture,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f61,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(flattening,[],[f60]) ).
fof(f77,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f78,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(flattening,[],[f77]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(flattening,[],[f98]) ).
fof(f138,plain,
aScalar0(xE),
inference(cnf_transformation,[],[f48]) ).
fof(f144,plain,
aScalar0(xH),
inference(cnf_transformation,[],[f51]) ).
fof(f147,plain,
xP = sdtasdt0(xE,xH),
inference(cnf_transformation,[],[f53]) ).
fof(f148,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f53]) ).
fof(f152,plain,
aScalar0(xN),
inference(cnf_transformation,[],[f55]) ).
fof(f156,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(cnf_transformation,[],[f61]) ).
fof(f162,plain,
! [X0,X1] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X0)
| ~ aScalar0(X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f182,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f305,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH)))
| ~ aScalar0(xE)
| ~ aScalar0(xH)
| ~ aScalar0(X0) ),
inference(superposition,[],[f156,f179]) ).
fof(f308,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH)))
| ~ aScalar0(xH)
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f305,f138]) ).
fof(f316,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH)))
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f308,f144]) ).
fof(f324,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))
| ~ aScalar0(X0) ),
inference(forward_demodulation,[],[f316,f147]) ).
fof(f489,plain,
! [X0] :
( sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH))) != sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))
| ~ aScalar0(X0)
| ~ aScalar0(xP)
| ~ aScalar0(xP)
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(superposition,[],[f324,f182]) ).
fof(f498,plain,
! [X0] :
( sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH))) != sdtpldt0(xP,sdtpldt0(xP,sdtasdt0(xH,xH)))
| ~ aScalar0(X0)
| ~ aScalar0(xP)
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(duplicate_literal_removal,[],[f489]) ).
fof(f499,plain,
! [X0] :
( ~ aScalar0(X0)
| ~ aScalar0(xP)
| ~ aScalar0(sdtasdt0(xH,xH)) ),
inference(trivial_inequality_removal,[],[f498]) ).
fof(f509,plain,
! [X0] :
( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(X0) ),
inference(forward_subsumption_resolution,[],[f499,f148]) ).
fof(f513,plain,
! [X0] :
( ~ aScalar0(X0)
| ~ aScalar0(xH)
| ~ aScalar0(xH) ),
inference(resolution,[],[f509,f162]) ).
fof(f515,plain,
! [X0] :
( ~ aScalar0(X0)
| ~ aScalar0(xH) ),
inference(duplicate_literal_removal,[],[f513]) ).
fof(f516,plain,
! [X0] : ~ aScalar0(X0),
inference(forward_subsumption_resolution,[],[f515,f144]) ).
fof(f543,plain,
$false,
inference(resolution,[],[f516,f152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG077+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n019.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 23:09:48 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.31/1.68 % (3510714)Detected formulas, will run a generic FOF schedule.
% 5.31/1.68 % (3510725)dis-21_1_sil=8000:lcm=predicate:random_seed=2277531715: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)
% 5.31/1.68 % (3510725)Instruction limit reached!
% 5.31/1.68 % (3510725)------------------------------
% 5.31/1.68 % (3510725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.68 % (3510725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.68 % (3510725)CaDiCaL version: 2.1.3
% 5.31/1.68 % (3510725)Termination reason: Instruction limit
% 5.31/1.68 % (3510725)Termination phase: Saturation
% 5.31/1.68 % (3510725)Time elapsed: 0.040 s
% 5.31/1.68 % (3510725)Peak memory usage: 89 MB
% 5.31/1.68 % (3510725)Instructions burned: 131 (million)
% 5.31/1.68 % (3510724)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=830995279:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.31/1.68 % (3510722)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2251223940:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.31/1.68 % (3510723)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1104184640:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.31/1.68 % (3510720)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=1414925455:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.31/1.68 % (3510719)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=2565420796:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.31/1.68 % (3510721)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=3905190983:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.31/1.68 % (3510723)First to succeed.
% 5.31/1.68 % (3510723)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3510714"
% 5.31/1.68 % (3510727)lrs+10_1_sil=8000:sp=occurrence:random_seed=227446711:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.31/1.68 % (3510724)Also succeeded, but the first one will report.
% 5.31/1.68 % (3510722)Also succeeded, but the first one will report.
% 5.31/1.68 % (3510727)Instruction limit reached!
% 5.31/1.68 % (3510727)------------------------------
% 5.31/1.68 % (3510727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.68 % (3510727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.68 % (3510727)CaDiCaL version: 2.1.3
% 5.31/1.68 % (3510727)Termination reason: Instruction limit
% 5.31/1.68 % (3510727)Termination phase: Saturation
% 5.31/1.68 % (3510727)Time elapsed: 0.136 s
% 5.31/1.68 % (3510727)Peak memory usage: 93 MB
% 5.31/1.68 % (3510727)Instructions burned: 286 (million)
% 5.31/1.68 % (3510735)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2657170651:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 5.31/1.68 % (3510723)Refutation found. Thanks to Tanya!
% 5.31/1.68 % SZS status Theorem for theBenchmark
% 5.31/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 5.31/1.68 % (3510723)------------------------------
% 5.31/1.68 % (3510723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.31/1.68 % (3510723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.31/1.68 % (3510723)CaDiCaL version: 2.1.3
% 5.31/1.68 % (3510723)Termination reason: Refutation
% 5.31/1.68 % (3510723)Time elapsed: 0.016 s
% 5.31/1.68 % (3510723)Peak memory usage: 88 MB
% 5.31/1.68 % (3510723)Instructions burned: 14 (million)
% 5.31/1.68 % (3510723)------------------------------
% 5.31/1.68 % (3510723)------------------------------
% 5.31/1.68 % (3510714)Success in time 0.683 s
% 5.31/1.68 % Vampire exiting
%------------------------------------------------------------------------------