%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL096-10 : 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 : n014.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 11:51:11 AM UTC 2026
% Result : Unsatisfiable 6.15s 1.74s
% Output : Refutation 6.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 105 ( 105 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0,X1] : ifeq(is_a_theorem(equivalent(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f3,plain,
! [X0,X1] : true = ifeq(is_a_theorem(equivalent(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_2) ).
fof(f5,plain,
! [X2,X3,X0,X1] : true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),equivalent(X1,X2)),X3),X3)),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_3) ).
fof(f7,plain,
! [X2,X3,X0,X1,X4] : true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4)),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] : is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X3),equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_4) ).
fof(f9,plain,
! [X2,X3,X0,X1,X4] : true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),X2),X3),equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3)))),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_1) ).
fof(f11,plain,
true != is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(b,b),a)),c),c)),
inference(reorient_equations,[],[f10]) ).
fof(f14,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3))),true),true),
inference(superposition,[],[f3,f9]) ).
fof(f15,plain,
! [X2,X3,X0,X1,X4,X5] : true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4),X5)),true,ifeq(true,true,is_a_theorem(X5),true),true),
inference(superposition,[],[f3,f7]) ).
fof(f23,plain,
! [X2,X3,X0,X1,X4,X5] : true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),equivalent(equivalent(X1,X2),X3)),X4),X4),X5)),true,is_a_theorem(X5),true),
inference(forward_demodulation,[],[f15,f1]) ).
fof(f24,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(X0,X1),X2),X3)),true,is_a_theorem(equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),X3))),true),
inference(forward_demodulation,[],[f14,f1]) ).
fof(f27,plain,
! [X2,X3,X0,X1,X4,X5] : true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X5),X4),equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X5),X4))),true),
inference(superposition,[],[f24,f7]) ).
fof(f28,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X0),X4),equivalent(equivalent(equivalent(X2,X3),X0),X4))),true),
inference(superposition,[],[f24,f5]) ).
fof(f34,plain,
! [X2,X3,X0,X1,X4] : true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),equivalent(X1,X3)),X0),X4),equivalent(equivalent(equivalent(X2,X3),X0),X4))),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4,X5] : true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X5),X4),equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X5),X4))),
inference(forward_demodulation,[],[f27,f1]) ).
fof(f44,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),equivalent(equivalent(X0,X1),X2))),X3),X3)),true),
inference(superposition,[],[f23,f35]) ).
fof(f52,plain,
! [X2,X3,X0,X1,X4] : true = is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X0,X4),X2),equivalent(equivalent(X1,X4),equivalent(equivalent(X0,X1),X2))),X3),X3)),
inference(forward_demodulation,[],[f44,f1]) ).
fof(f107,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(true,true,ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X4)),true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),X4)),true),true),
inference(superposition,[],[f3,f34]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] : true = ifeq(is_a_theorem(equivalent(equivalent(equivalent(equivalent(X0,X1),equivalent(X0,X2)),X3),X4)),true,is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),X4)),true),
inference(forward_demodulation,[],[f107,f1]) ).
fof(f172,plain,
! [X2,X3,X0] : true = ifeq(true,true,is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(equivalent(X0,X0),X2)),X3),X3)),true),
inference(superposition,[],[f113,f52]) ).
fof(f198,plain,
! [X2,X3,X0] : true = is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(equivalent(X0,X0),X2)),X3),X3)),
inference(forward_demodulation,[],[f172,f1]) ).
fof(f199,plain,
$false,
inference(backward_subsumption_resolution,[],[f11,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 15:21:31 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 6.15/1.74 % (930660)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.15/1.74 % (930676)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=866845577:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 6.15/1.74 % (930673)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3462453688:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 6.15/1.74 % (930676)Instruction limit reached!
% 6.15/1.74 % (930676)------------------------------
% 6.15/1.74 % (930676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.15/1.74 % (930676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.15/1.74 % (930676)CaDiCaL version: 2.1.3
% 6.15/1.74 % (930676)Termination reason: Instruction limit
% 6.15/1.74 % (930676)Termination phase: Saturation
% 6.15/1.74 % (930676)Time elapsed: 0.051 s
% 6.15/1.74 % (930676)Peak memory usage: 89 MB
% 6.15/1.74 % (930676)Instructions burned: 136 (million)
% 6.15/1.74 % (930677)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1393899604:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 6.15/1.74 % (930675)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3580017025:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 6.15/1.74 % (930674)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=559781086:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 6.15/1.74 % (930678)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3732909439:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 6.15/1.74 % (930679)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1131162284:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 6.15/1.74 % (930683)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3014431909:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 6.15/1.74 % (930677)Instruction limit reached!
% 6.15/1.74 % (930677)------------------------------
% 6.15/1.74 % (930677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.15/1.74 % (930677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.15/1.74 % (930677)CaDiCaL version: 2.1.3
% 6.15/1.74 % (930677)Termination reason: Instruction limit
% 6.15/1.74 % (930677)Termination phase: Saturation
% 6.15/1.74 % (930677)Time elapsed: 0.094 s
% 6.15/1.74 % (930677)Peak memory usage: 89 MB
% 6.15/1.74 % (930677)Instructions burned: 182 (million)
% 6.15/1.74 % (930678)Instruction limit reached!
% 6.15/1.74 % (930678)------------------------------
% 6.15/1.74 % (930678)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.15/1.74 % (930678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.15/1.74 % (930678)CaDiCaL version: 2.1.3
% 6.15/1.74 % (930678)Termination reason: Instruction limit
% 6.15/1.74 % (930678)Termination phase: Saturation
% 6.15/1.74 % (930678)Time elapsed: 0.203 s
% 6.15/1.74 % (930678)Peak memory usage: 90 MB
% 6.15/1.74 % (930678)Instructions burned: 257 (million)
% 6.15/1.74 % (930690)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2071731164:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.15/1.74 % (930693)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=4174620526:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.15/1.74 % (930683)First to succeed.
% 6.15/1.74 % (930683)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-930660"
% 6.15/1.74 % (930693)Instruction limit reached!
% 6.15/1.74 % (930693)------------------------------
% 6.15/1.74 % (930693)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.15/1.74 % (930693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.15/1.74 % (930693)CaDiCaL version: 2.1.3
% 6.15/1.74 % (930693)Termination reason: Instruction limit
% 6.15/1.74 % (930693)Termination phase: Saturation
% 6.15/1.74 % (930693)Time elapsed: 0.115 s
% 6.15/1.74 % (930693)Peak memory usage: 88 MB
% 6.15/1.74 % (930693)Instructions burned: 215 (million)
% 6.15/1.74 % (930749)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=969959384:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 6.15/1.74 % (930683)Refutation found. Thanks to Tanya!
% 6.15/1.74 % SZS status Unsatisfiable for theBenchmark
% 6.15/1.74 % SZS output start Proof for theBenchmark
% See solution above
% 6.15/1.74 % (930683)------------------------------
% 6.15/1.74 % (930683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.15/1.74 % (930683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.15/1.74 % (930683)CaDiCaL version: 2.1.3
% 6.15/1.74 % (930683)Termination reason: Refutation
% 6.15/1.74 % (930683)Time elapsed: 0.390 s
% 6.15/1.74 % (930683)Peak memory usage: 129 MB
% 6.15/1.74 % (930683)Instructions burned: 1034 (million)
% 6.15/1.74 % (930683)------------------------------
% 6.15/1.74 % (930683)------------------------------
% 6.15/1.74 % (930660)Success in time 0.806 s
% 6.15/1.74 % Vampire exiting
%------------------------------------------------------------------------------