%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN082+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:26:46 PM UTC 2026
% Result : Theorem 3.56s 1.48s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 32 unt; 0 def)
% Number of atoms : 117 ( 41 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 101 ( 39 ~; 24 |; 38 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 109 ( 87 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f4,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r4(X0,X1,X3)
& X3 != X2 )
| ( r4(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
fof(f6,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r4(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f9,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( r1(X3)
& X1 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
fof(f12,conjecture,
? [X0,X1] :
( ? [X2] :
( r4(X0,X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& X1 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xtimesoneeqzero) ).
fof(f13,negated_conjecture,
~ ? [X0,X1] :
( ? [X2] :
( r4(X0,X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& X1 = X4 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( ~ r4(X0,X2,X1)
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X2) ) )
| ! [X4] :
( ~ r1(X4)
| X1 != X4 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f17,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK2(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK2(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f3]) ).
fof(f18,plain,
! [X0,X1,X3] :
( ( ~ r4(X0,X1,X3)
& sK3(X0,X1) != X3 )
| ( r4(X0,X1,X3)
& sK3(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( r2(X1,sK10(X0,X1))
& r4(X0,sK10(X0,X1),sK9(X0,X1))
& sK8(X0,X1) = sK9(X0,X1)
& r3(sK11(X0,X1),X0,sK8(X0,X1))
& r4(X0,X1,sK11(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1)),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f6]) ).
fof(f21,plain,
! [X0] :
( r1(sK13(X0))
& r3(X0,sK13(X0),sK12(X0))
& sK12(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f8]) ).
fof(f22,plain,
! [X0] :
( r1(sK15(X0))
& r4(X0,sK15(X0),sK14(X0))
& r1(sK16(X0))
& sK14(X0) = sK16(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X1,sK14(X0)),skolemize(X2,sK15(X0)),skolemize(X3,sK16(X0))],[f9]) ).
fof(f25,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X3,X0,X1] :
( ~ r3(X0,X1,X3)
| sK2(X0,X1) = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f38,plain,
! [X3,X0,X1] :
( ~ r4(X0,X1,X3)
| sK3(X0,X1) = X3 ),
inference(cnf_transformation,[],[f18]) ).
fof(f45,plain,
! [X0,X1] : r4(X0,X1,sK11(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f46,plain,
! [X0,X1] : r3(sK11(X0,X1),X0,sK8(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f47,plain,
! [X0,X1] : sK8(X0,X1) = sK9(X0,X1),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] : r4(X0,sK10(X0,X1),sK9(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f49,plain,
! [X0,X1] : r2(X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f51,plain,
! [X0] : sK12(X0) = X0,
inference(cnf_transformation,[],[f21]) ).
fof(f52,plain,
! [X0] : r3(X0,sK13(X0),sK12(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f53,plain,
! [X0] : r1(sK13(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0] : sK14(X0) = sK16(X0),
inference(cnf_transformation,[],[f22]) ).
fof(f55,plain,
! [X0] : r1(sK16(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0] : r4(X0,sK15(X0),sK14(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f57,plain,
! [X0] : r1(sK15(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4] :
( ~ r4(X0,X2,X1)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r1(X4)
| X1 != X4 ),
inference(cnf_transformation,[],[f14]) ).
fof(f64,plain,
r1(sK0),
inference(equality_resolution,[],[f25]) ).
fof(f74,plain,
! [X2,X3,X0,X4] :
( ~ r1(X3)
| ~ r4(X0,X2,X4)
| ~ r2(X3,X2)
| ~ r1(X4) ),
inference(equality_resolution,[],[f63]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ r2(sK0,X1)
| ~ r4(X0,X1,X2)
| ~ r1(X2) ),
inference(resolution,[],[f64,f74]) ).
fof(f89,plain,
! [X0] : sK0 = sK13(X0),
inference(resolution,[],[f26,f53]) ).
fof(f90,plain,
! [X0] : sK0 = sK15(X0),
inference(resolution,[],[f26,f57]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ r4(X0,sK10(X1,sK0),X2)
| ~ r1(X2) ),
inference(resolution,[],[f49,f77]) ).
fof(f101,plain,
! [X0] : r1(sK14(X0)),
inference(superposition,[],[f55,f54]) ).
fof(f107,plain,
! [X0] : r3(X0,sK13(X0),X0),
inference(forward_demodulation,[],[f52,f51]) ).
fof(f121,plain,
! [X0,X1] : r4(X0,sK10(X0,X1),sK8(X0,X1)),
inference(forward_demodulation,[],[f48,f47]) ).
fof(f127,plain,
! [X0] : ~ r1(sK8(X0,sK0)),
inference(resolution,[],[f121,f96]) ).
fof(f130,plain,
! [X0] : sK2(X0,sK13(X0)) = X0,
inference(resolution,[],[f34,f107]) ).
fof(f132,plain,
! [X0,X1] : sK8(X0,X1) = sK2(sK11(X0,X1),X0),
inference(resolution,[],[f34,f46]) ).
fof(f136,plain,
! [X0,X1] : sK3(X0,X1) = sK11(X0,X1),
inference(resolution,[],[f38,f45]) ).
fof(f138,plain,
! [X0] : sK14(X0) = sK3(X0,sK15(X0)),
inference(resolution,[],[f38,f56]) ).
fof(f157,plain,
! [X0] : sK0 = sK14(X0),
inference(resolution,[],[f101,f26]) ).
fof(f216,plain,
! [X0] : sK2(X0,sK0) = X0,
inference(forward_demodulation,[],[f130,f89]) ).
fof(f248,plain,
! [X0] : sK14(X0) = sK3(X0,sK0),
inference(forward_demodulation,[],[f138,f90]) ).
fof(f249,plain,
! [X0] : sK0 = sK3(X0,sK0),
inference(forward_demodulation,[],[f248,f157]) ).
fof(f289,plain,
! [X0,X1] : sK8(X0,X1) = sK2(sK3(X0,X1),X0),
inference(forward_demodulation,[],[f132,f136]) ).
fof(f308,plain,
! [X0] : sK3(sK0,X0) = sK8(sK0,X0),
inference(superposition,[],[f289,f216]) ).
fof(f424,plain,
~ r1(sK3(sK0,sK0)),
inference(superposition,[],[f127,f308]) ).
fof(f426,plain,
~ r1(sK0),
inference(forward_demodulation,[],[f424,f249]) ).
fof(f431,plain,
$false,
inference(forward_subsumption_resolution,[],[f426,f64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN082+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 21:58:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.56/1.47 % (208830)Detected formulas, will run a generic FOF schedule.
% 3.56/1.47 % (208838)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3431310183:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.56/1.47 % (208838)Refutation not found, incomplete strategy
% 3.56/1.47 % (208838)------------------------------
% 3.56/1.47 % (208838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.47 % (208838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.47 % (208838)CaDiCaL version: 2.1.3
% 3.56/1.47 % (208838)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.47 % (208838)Time elapsed: 0.001 s
% 3.56/1.47 % (208838)Peak memory usage: 88 MB
% 3.56/1.47 % (208838)Instructions burned: 1 (million)
% 3.56/1.47 % (208835)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=3927564353:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.56/1.47 % (208839)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1051048736:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.56/1.48 % (208841)dis-21_1_sil=8000:lcm=predicate:random_seed=2657270824: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)
% 3.56/1.48 % (208836)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=2173677007:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.56/1.48 % (208837)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=777164905:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.56/1.48 % (208840)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3143100250:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.56/1.48 % (208841)Refutation not found, incomplete strategy
% 3.56/1.48 % (208841)------------------------------
% 3.56/1.48 % (208841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (208841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (208841)CaDiCaL version: 2.1.3
% 3.56/1.48 % (208841)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.48 % (208841)Time elapsed: 0.002 s
% 3.56/1.48 % (208841)Peak memory usage: 88 MB
% 3.56/1.48 % (208841)Instructions burned: 2 (million)
% 3.56/1.48 % (208840)First to succeed.
% 3.56/1.48 % (208840)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-208830"
% 3.56/1.48 % (208839)Instruction limit reached!
% 3.56/1.48 % (208839)------------------------------
% 3.56/1.48 % (208839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (208839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (208839)CaDiCaL version: 2.1.3
% 3.56/1.48 % (208839)Termination reason: Instruction limit
% 3.56/1.48 % (208839)Termination phase: Saturation
% 3.56/1.48 % (208839)Time elapsed: 0.072 s
% 3.56/1.48 % (208839)Peak memory usage: 88 MB
% 3.56/1.48 % (208839)Instructions burned: 119 (million)
% 3.56/1.48 % (208838)------------------------------
% 3.56/1.48 % (208838)------------------------------
% 3.56/1.48 % (208850)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2260950761:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.56/1.48 % (208850)Refutation not found, incomplete strategy
% 3.56/1.48 % (208850)------------------------------
% 3.56/1.48 % (208850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (208850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (208850)CaDiCaL version: 2.1.3
% 3.56/1.48 % (208850)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.48 % (208850)Time elapsed: 0.003 s
% 3.56/1.48 % (208850)Peak memory usage: 89 MB
% 3.56/1.48 % (208850)Instructions burned: 7 (million)
% 3.56/1.48 % (208849)lrs+10_1_sil=8000:sp=occurrence:random_seed=2222357163:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.56/1.48 % (208841)------------------------------
% 3.56/1.48 % (208841)------------------------------
% 3.56/1.48 % (208840)Refutation found. Thanks to Tanya!
% 3.56/1.48 % SZS status Theorem for theBenchmark
% 3.56/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.48 % (208840)------------------------------
% 3.56/1.48 % (208840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.48 % (208840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.48 % (208840)CaDiCaL version: 2.1.3
% 3.56/1.48 % (208840)Termination reason: Refutation
% 3.56/1.48 % (208840)Time elapsed: 0.013 s
% 3.56/1.48 % (208840)Peak memory usage: 89 MB
% 3.56/1.48 % (208840)Instructions burned: 16 (million)
% 3.56/1.48 % (208840)------------------------------
% 3.56/1.48 % (208840)------------------------------
% 3.56/1.48 % (208830)Success in time 0.422 s
% 3.56/1.48 % Vampire exiting
%------------------------------------------------------------------------------