%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:46:14 PM UTC 2026
% Result : Unsatisfiable 6.41s 2.15s
% Output : Refutation 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 34 ( 31 unt; 0 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-4 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : aux(X0,X1,X2,btrue) = union(X2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom) ).
fof(f3,axiom,
! [X0] : barbar(btrue,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
fof(f4,plain,
! [X0] : btrue = barbar(btrue,X0),
inference(reorient_equations,[],[f3]) ).
fof(f11,axiom,
eqNat(z,z) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
fof(f12,plain,
btrue = eqNat(z,z),
inference(reorient_equations,[],[f11]) ).
fof(f15,axiom,
! [X2,X0,X1] : elem(X0,cons(X1,X2)) = barbar(eqNat(X0,X1),elem(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_009) ).
fof(f16,axiom,
! [X0] : union(nil,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_010) ).
fof(f17,axiom,
! [X2,X0,X1] : union(cons(X0,X1),X2) = aux(X2,X0,X1,elem(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_011) ).
fof(f18,axiom,
! [X0,X1] : prop_union_comm(X0,X1) = eq(union(X0,X1),union(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_012) ).
fof(f30,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_019) ).
fof(f31,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f30]) ).
fof(f32,axiom,
! [X0] : eq3(X0,X0) = btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_020) ).
fof(f33,plain,
! [X0] : btrue = eq3(X0,X0),
inference(reorient_equations,[],[f32]) ).
fof(f36,axiom,
! [X2,X3,X0,X1] :
( eq2(X0,X1) != btrue
| eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_022) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( btrue != eq2(X0,X1)
| eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3) ),
inference(reorient_equations,[],[f36]) ).
fof(f40,axiom,
! [X0,X1] : eq(cons(X0,X1),nil) = bfalse,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_024) ).
fof(f41,plain,
! [X0,X1] : bfalse = eq(cons(X0,X1),nil),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
! [X0,X1] : eq3(prop_union_comm(X0,X1),bfalse) != btrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f43,plain,
! [X0,X1] : btrue != eq3(prop_union_comm(X0,X1),bfalse),
inference(reorient_equations,[],[f42]) ).
fof(f52,plain,
! [X0] : elem(z,cons(z,X0)) = barbar(btrue,elem(z,X0)),
inference(superposition,[],[f15,f12]) ).
fof(f59,plain,
! [X0] : btrue = elem(z,cons(z,X0)),
inference(forward_demodulation,[],[f52,f4]) ).
fof(f68,plain,
! [X0,X1] : union(cons(z,X0),cons(z,X1)) = aux(cons(z,X1),z,X0,btrue),
inference(superposition,[],[f17,f59]) ).
fof(f70,plain,
! [X0,X1] : union(cons(z,X0),cons(z,X1)) = union(X0,cons(z,X1)),
inference(forward_demodulation,[],[f68,f1]) ).
fof(f71,plain,
! [X2,X0,X1] :
( btrue != btrue
| eq(cons(X0,X1),cons(X0,X2)) = eq(X1,X2) ),
inference(superposition,[],[f37,f31]) ).
fof(f75,plain,
! [X2,X0,X1] : eq(cons(X0,X1),cons(X0,X2)) = eq(X1,X2),
inference(trivial_inequality_removal,[],[f71]) ).
fof(f148,plain,
! [X0,X1] : prop_union_comm(cons(z,X0),cons(z,X1)) = eq(union(X0,cons(z,X1)),union(cons(z,X1),cons(z,X0))),
inference(superposition,[],[f18,f70]) ).
fof(f149,plain,
! [X0,X1] : prop_union_comm(cons(z,X0),cons(z,X1)) = eq(union(X0,cons(z,X1)),union(X1,cons(z,X0))),
inference(forward_demodulation,[],[f148,f70]) ).
fof(f483,plain,
! [X0] : prop_union_comm(cons(z,nil),cons(z,X0)) = eq(cons(z,X0),union(X0,cons(z,nil))),
inference(superposition,[],[f149,f16]) ).
fof(f494,plain,
! [X0] : prop_union_comm(cons(z,nil),cons(z,cons(z,X0))) = eq(cons(z,cons(z,X0)),union(X0,cons(z,nil))),
inference(superposition,[],[f483,f70]) ).
fof(f1062,plain,
prop_union_comm(cons(z,nil),cons(z,cons(z,nil))) = eq(cons(z,cons(z,nil)),cons(z,nil)),
inference(superposition,[],[f494,f16]) ).
fof(f1065,plain,
prop_union_comm(cons(z,nil),cons(z,cons(z,nil))) = eq(cons(z,nil),nil),
inference(forward_demodulation,[],[f1062,f75]) ).
fof(f1066,plain,
bfalse = prop_union_comm(cons(z,nil),cons(z,cons(z,nil))),
inference(forward_demodulation,[],[f1065,f41]) ).
fof(f1094,plain,
btrue != eq3(bfalse,bfalse),
inference(superposition,[],[f43,f1066]) ).
fof(f1095,plain,
$false,
inference(forward_subsumption_resolution,[],[f1094,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWX228-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.31 % Computer : n007.cluster.edu
% 0.29/0.31 % Model : x86_64 x86_64
% 0.29/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.29/0.31 % Memory : 8046.5625MB
% 0.29/0.31 % OS : Linux 6.8.0-71-generic
% 0.29/0.31 % CPULimit : 300
% 0.29/0.31 % WCLimit : 300
% 0.29/0.31 % DateTime : Mon Sep 28 15:11:25 UTC 2026
% 0.29/0.31 % CPUTime :
% 0.29/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.29/0.37 Running first-order theorem proving
% 0.29/0.37 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
% 6.41/2.15 % (2488203)Input is clausal, will run a generic CNF schedule.
% 6.41/2.15 % (2488225)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=3838309439:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.41/2.15 % (2488228)lrs+10_1_sil=8000:sp=occurrence:random_seed=914732797:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.41/2.15 % (2488227)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1788189075:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.41/2.15 % (2488226)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1775593037:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.41/2.15 % (2488229)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2408344313:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.41/2.15 % (2488230)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4111181968:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.41/2.15 % (2488231)dis-21_1_sil=8000:lcm=predicate:random_seed=2697547114:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 6.41/2.15 % (2488231)Refutation not found, incomplete strategy
% 6.41/2.15 % (2488231)------------------------------
% 6.41/2.15 % (2488231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.15 % (2488231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.15 % (2488231)CaDiCaL version: 2.1.3
% 6.41/2.15 % (2488231)Termination reason: Refutation not found, incomplete strategy
% 6.41/2.15 % (2488231)Time elapsed: 0.003 s
% 6.41/2.15 % (2488231)Peak memory usage: 88 MB
% 6.41/2.15 % (2488231)Instructions burned: 1 (million)
% 6.41/2.15 % (2488230)First to succeed.
% 6.41/2.15 % (2488230)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2488203"
% 6.41/2.15 % (2488228)Instruction limit reached!
% 6.41/2.15 % (2488228)------------------------------
% 6.41/2.15 % (2488228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.15 % (2488228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.15 % (2488228)CaDiCaL version: 2.1.3
% 6.41/2.15 % (2488228)Termination reason: Instruction limit
% 6.41/2.15 % (2488228)Termination phase: Saturation
% 6.41/2.15 % (2488228)Time elapsed: 0.094 s
% 6.41/2.15 % (2488228)Peak memory usage: 88 MB
% 6.41/2.15 % (2488228)Instructions burned: 107 (million)
% 6.41/2.15 % (2488229)Instruction limit reached!
% 6.41/2.15 % (2488229)------------------------------
% 6.41/2.15 % (2488229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.15 % (2488229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.15 % (2488229)CaDiCaL version: 2.1.3
% 6.41/2.15 % (2488229)Termination reason: Instruction limit
% 6.41/2.15 % (2488229)Termination phase: Saturation
% 6.41/2.15 % (2488229)Time elapsed: 0.116 s
% 6.41/2.15 % (2488229)Peak memory usage: 89 MB
% 6.41/2.15 % (2488229)Instructions burned: 115 (million)
% 6.41/2.15 % (2488239)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1900924494:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 6.41/2.15 % (2488239)Refutation not found, incomplete strategy
% 6.41/2.15 % (2488239)------------------------------
% 6.41/2.15 % (2488239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.15 % (2488239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.15 % (2488239)CaDiCaL version: 2.1.3
% 6.41/2.15 % (2488239)Termination reason: Refutation not found, incomplete strategy
% 6.41/2.15 % (2488239)Time elapsed: 0.003 s
% 6.41/2.15 % (2488239)Peak memory usage: 88 MB
% 6.41/2.15 % (2488239)Instructions burned: 1 (million)
% 6.41/2.15 % (2488231)------------------------------
% 6.41/2.15 % (2488231)------------------------------
% 6.41/2.15 % (2488240)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2648320344:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2995 on theBenchmark for (2995ds/189Mi)
% 6.41/2.15 % (2488240)Refutation not found, incomplete strategy
% 6.41/2.15 % (2488240)------------------------------
% 6.41/2.15 % (2488240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.15 % (2488240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.15 % (2488240)CaDiCaL version: 2.1.3
% 6.41/2.15 % (2488240)Termination reason: Refutation not found, incomplete strategy
% 6.41/2.15 % (2488240)Time elapsed: 0.004 s
% 6.41/2.15 % (2488240)Peak memory usage: 88 MB
% 6.41/2.15 % (2488240)Instructions burned: 2 (million)
% 6.41/2.15 % (2488230)Refutation found. Thanks to Tanya!
% 6.41/2.15 % SZS status Unsatisfiable for theBenchmark
% 6.41/2.15 % SZS output start Proof for theBenchmark
% See solution above
% 6.41/2.15 % (2488230)------------------------------
% 6.41/2.15 % (2488230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/2.15 % (2488230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/2.15 % (2488230)CaDiCaL version: 2.1.3
% 6.41/2.15 % (2488230)Termination reason: Refutation
% 6.41/2.15 % (2488230)Time elapsed: 0.054 s
% 6.41/2.15 % (2488230)Peak memory usage: 89 MB
% 6.41/2.15 % (2488230)Instructions burned: 54 (million)
% 6.41/2.15 % (2488230)------------------------------
% 6.41/2.15 % (2488230)------------------------------
% 6.41/2.15 % (2488203)Success in time 0.758 s
% 6.41/2.15 % Vampire exiting
%------------------------------------------------------------------------------