%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 12:42:24 PM UTC 2026
% Result : Theorem 2.57s 1.36s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 5 unt; 0 def)
% Number of atoms : 133 ( 39 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 163 ( 61 ~; 62 |; 30 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 104 ( 82 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = cartesian_product2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f8,conjecture,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
<=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
=> cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
<=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
=> cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f11,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
& ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
<=> in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
? [X0,X1,X2,X3] :
( cartesian_product2(X0,X1) != cartesian_product2(X2,X3)
& ! [X4,X5] :
( ( in(ordered_pair(X4,X5),cartesian_product2(X0,X1))
| ~ in(ordered_pair(X4,X5),cartesian_product2(X2,X3)) )
& ( in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
| ~ in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) ) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f15,plain,
( cartesian_product2(sK0,sK1) != cartesian_product2(sK2,sK3)
& ! [X4,X5] :
( ( in(ordered_pair(X4,X5),cartesian_product2(sK0,sK1))
| ~ in(ordered_pair(X4,X5),cartesian_product2(sK2,sK3)) )
& ( in(ordered_pair(X4,X5),cartesian_product2(sK2,sK3))
| ~ in(ordered_pair(X4,X5),cartesian_product2(sK0,sK1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK4(X0,X1),X1)
| ~ in(sK4(X0,X1),X0) )
& ( in(sK4(X0,X1),X1)
| in(sK4(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 ) )
& ( ? [X4,X5] :
( in(X4,X0)
& in(X5,X1)
& X3 = ordered_pair(X4,X5) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ? [X3] :
( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( in(X6,X0)
& in(X7,X1)
& ordered_pair(X6,X7) = X3 )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ? [X11,X12] :
( in(X11,X0)
& in(X12,X1)
& ordered_pair(X11,X12) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( X2 = cartesian_product2(X0,X1)
| ( ( ! [X4,X5] :
( ~ in(X4,X0)
| ~ in(X5,X1)
| ordered_pair(X4,X5) != sK5(X0,X1,X2) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK6(X0,X1,X2),X0)
& in(sK7(X0,X1,X2),X1)
& sK5(X0,X1,X2) = ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2)) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ~ in(X9,X0)
| ~ in(X10,X1)
| ordered_pair(X9,X10) != X8 ) )
& ( ( in(sK8(X0,X1,X8),X0)
& in(sK9(X0,X1,X8),X1)
& ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8 )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X3,sK5(X0,X1,X2)),skolemize(X6,sK6(X0,X1,X2)),skolemize(X7,sK7(X0,X1,X2)),skolemize(X11,sK8(X0,X1,X8)),skolemize(X12,sK9(X0,X1,X8))],[f19]) ).
fof(f21,plain,
! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(sK2,sK3))
| ~ in(ordered_pair(X4,X5),cartesian_product2(sK0,sK1)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(sK0,sK1))
| ~ in(ordered_pair(X4,X5),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f23,plain,
cartesian_product2(sK0,sK1) != cartesian_product2(sK2,sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
! [X0,X1] :
( in(sK4(X0,X1),X1)
| X0 = X1
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| X0 = X1
| ~ in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1,X8] :
( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f27]) ).
fof(f54,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(sK2,sK3))
| ~ in(X0,cartesian_product2(sK0,sK1))
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[],[f21,f39]) ).
fof(f55,plain,
! [X2,X0,X1] :
( in(X0,cartesian_product2(sK0,sK1))
| ~ in(X0,cartesian_product2(sK2,sK3))
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(superposition,[],[f22,f39]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ in(sK4(X0,cartesian_product2(sK2,sK3)),cartesian_product2(sK0,sK1))
| ~ in(sK4(X0,cartesian_product2(sK2,sK3)),cartesian_product2(X1,X2))
| cartesian_product2(sK2,sK3) = X0
| ~ in(sK4(X0,cartesian_product2(sK2,sK3)),X0) ),
inference(resolution,[],[f54,f25]) ).
fof(f125,plain,
! [X0] :
( ~ in(sK4(X0,cartesian_product2(sK2,sK3)),cartesian_product2(sK0,sK1))
| cartesian_product2(sK2,sK3) = X0
| ~ in(sK4(X0,cartesian_product2(sK2,sK3)),X0) ),
inference(factoring,[],[f64]) ).
fof(f133,plain,
( ~ in(sK4(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),cartesian_product2(sK0,sK1))
| cartesian_product2(sK0,sK1) = cartesian_product2(sK2,sK3) ),
inference(factoring,[],[f125]) ).
fof(f135,plain,
~ in(sK4(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),cartesian_product2(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f133,f23]) ).
fof(f142,plain,
! [X0,X1] :
( ~ in(sK4(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),cartesian_product2(sK2,sK3))
| ~ in(sK4(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),cartesian_product2(X0,X1)) ),
inference(resolution,[],[f135,f55]) ).
fof(f168,plain,
~ in(sK4(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),cartesian_product2(sK2,sK3)),
inference(factoring,[],[f142]) ).
fof(f172,plain,
( cartesian_product2(sK0,sK1) = cartesian_product2(sK2,sK3)
| in(sK4(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),cartesian_product2(sK0,sK1)) ),
inference(resolution,[],[f168,f24]) ).
fof(f173,plain,
in(sK4(cartesian_product2(sK0,sK1),cartesian_product2(sK2,sK3)),cartesian_product2(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f172,f23]) ).
fof(f174,plain,
$false,
inference(forward_subsumption_resolution,[],[f173,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET955+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 % Computer : n011.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Mon Sep 28 03:16:16 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.45 Running first-order theorem proving
% 0.13/0.45 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
% 2.57/1.36 % (2983690)Detected formulas, will run a generic FOF schedule.
% 2.57/1.36 % (2983702)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1334825280:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.57/1.36 % (2983702)First to succeed.
% 2.57/1.36 % (2983702)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2983690"
% 2.57/1.36 % (2983704)dis-21_1_sil=8000:lcm=predicate:random_seed=4036895458: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)
% 2.57/1.36 % (2983701)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4186335591:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.57/1.36 % (2983699)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=3425655894:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.57/1.36 % (2983698)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=2142622190:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.57/1.36 % (2983700)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=1522493891:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.57/1.36 % (2983704)Refutation not found, incomplete strategy
% 2.57/1.36 % (2983704)------------------------------
% 2.57/1.36 % (2983704)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.36 % (2983704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.36 % (2983704)CaDiCaL version: 2.1.3
% 2.57/1.36 % (2983704)Termination reason: Refutation not found, incomplete strategy
% 2.57/1.36 % (2983704)Time elapsed: 0.005 s
% 2.57/1.36 % (2983704)Peak memory usage: 88 MB
% 2.57/1.36 % (2983704)Instructions burned: 5 (million)
% 2.57/1.36 % (2983701)Also succeeded, but the first one will report.
% 2.57/1.36 % (2983703)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1728640189:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.57/1.36 % (2983703)Instruction limit reached!
% 2.57/1.36 % (2983703)------------------------------
% 2.57/1.36 % (2983703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.36 % (2983703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.36 % (2983703)CaDiCaL version: 2.1.3
% 2.57/1.36 % (2983703)Termination reason: Instruction limit
% 2.57/1.36 % (2983703)Termination phase: Saturation
% 2.57/1.36 % (2983703)Time elapsed: 0.086 s
% 2.57/1.36 % (2983703)Peak memory usage: 89 MB
% 2.57/1.36 % (2983703)Instructions burned: 139 (million)
% 2.57/1.36 % (2983702)Refutation found. Thanks to Tanya!
% 2.57/1.36 % SZS status Theorem for theBenchmark
% 2.57/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.36 % (2983702)------------------------------
% 2.57/1.36 % (2983702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.36 % (2983702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.36 % (2983702)CaDiCaL version: 2.1.3
% 2.57/1.36 % (2983702)Termination reason: Refutation
% 2.57/1.36 % (2983702)Time elapsed: 0.004 s
% 2.57/1.36 % (2983702)Peak memory usage: 88 MB
% 2.57/1.36 % (2983702)Instructions burned: 10 (million)
% 2.57/1.36 % (2983702)------------------------------
% 2.57/1.36 % (2983702)------------------------------
% 2.57/1.36 % (2983690)Success in time 0.268 s
% 2.57/1.36 % Vampire exiting
%------------------------------------------------------------------------------