%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL057-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:37:46 AM UTC 2026
% Result : Unsatisfiable 6.26s 1.87s
% Output : Refutation 6.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f4,axiom,
! [X0] : apply(i,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
fof(f5,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f44,plain,
! [X0,X1] : apply(apply(apply(s,i),X1),X0) = apply(X0,apply(X1,X0)),
inference(superposition,[],[f1,f4]) ).
fof(f54,plain,
! [X2,X0,X1] : apply(X0,apply(X1,apply(X2,X1))) = apply(apply(apply(s,apply(b,X0)),X2),X1),
inference(superposition,[],[f1,f2]) ).
fof(f145,plain,
! [X0] : apply(X0,f(X0)) != apply(apply(apply(s,i),X0),f(X0)),
inference(superposition,[],[f5,f44]) ).
fof(f326,plain,
! [X0,X1] : apply(apply(X1,apply(X0,X1)),f(apply(X1,apply(X0,X1)))) != apply(apply(apply(apply(s,apply(b,apply(s,i))),X0),X1),f(apply(X1,apply(X0,X1)))),
inference(superposition,[],[f145,f54]) ).
fof(f417,plain,
! [X0] : apply(apply(X0,X0),f(apply(X0,X0))) != apply(apply(apply(apply(s,apply(b,apply(s,i))),i),X0),f(apply(X0,X0))),
inference(superposition,[],[f326,f4]) ).
fof(f451,plain,
$false,
inference(equality_resolution,[],[f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL057-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.23 % Computer : n016.cluster.edu
% 0.11/0.23 % Model : x86_64 x86_64
% 0.11/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.23 % Memory : 8046.5625MB
% 0.11/0.23 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Mon Sep 28 21:36:18 UTC 2026
% 0.11/0.24 % CPUTime :
% 0.11/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running first-order theorem proving
% 0.24/0.29 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
% 6.26/1.87 % (4049872)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.26/1.87 % (4049879)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3291971418:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.26/1.87 % (4049882)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2362071099:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.26/1.87 % (4049881)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2638669013:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.26/1.87 % (4049880)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1310102568:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.26/1.87 % (4049878)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=2368678698:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.26/1.87 % (4049877)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=1372488807:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.26/1.87 % (4049883)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=474176161:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.26/1.87 % (4049883)First to succeed.
% 6.26/1.87 % (4049883)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4049872"
% 6.26/1.87 % (4049880)Instruction limit reached!
% 6.26/1.87 % (4049880)------------------------------
% 6.26/1.87 % (4049880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.26/1.87 % (4049880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.87 % (4049880)CaDiCaL version: 2.1.3
% 6.26/1.87 % (4049880)Termination reason: Instruction limit
% 6.26/1.87 % (4049880)Termination phase: Saturation
% 6.26/1.87 % (4049880)Time elapsed: 0.129 s
% 6.26/1.87 % (4049880)Peak memory usage: 89 MB
% 6.26/1.87 % (4049880)Instructions burned: 137 (million)
% 6.26/1.87 % (4049881)Instruction limit reached!
% 6.26/1.87 % (4049881)------------------------------
% 6.26/1.87 % (4049881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.26/1.87 % (4049881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.87 % (4049881)CaDiCaL version: 2.1.3
% 6.26/1.87 % (4049881)Termination reason: Instruction limit
% 6.26/1.87 % (4049881)Termination phase: Saturation
% 6.26/1.87 % (4049881)Time elapsed: 0.142 s
% 6.26/1.87 % (4049881)Peak memory usage: 89 MB
% 6.26/1.87 % (4049881)Instructions burned: 183 (million)
% 6.26/1.87 % (4049882)Instruction limit reached!
% 6.26/1.87 % (4049882)------------------------------
% 6.26/1.87 % (4049882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.26/1.87 % (4049882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.87 % (4049882)CaDiCaL version: 2.1.3
% 6.26/1.87 % (4049882)Termination reason: Instruction limit
% 6.26/1.87 % (4049882)Termination phase: Saturation
% 6.26/1.87 % (4049882)Time elapsed: 0.263 s
% 6.26/1.87 % (4049882)Peak memory usage: 90 MB
% 6.26/1.87 % (4049882)Instructions burned: 257 (million)
% 6.26/1.87 % (4049891)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=342057151:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 6.26/1.87 % (4049892)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2879438586:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 6.26/1.87 % (4049893)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3660047157:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 6.26/1.87 % (4049883)Refutation found. Thanks to Tanya!
% 6.26/1.87 % SZS status Unsatisfiable for theBenchmark
% 6.26/1.87 % SZS output start Proof for theBenchmark
% See solution above
% 6.26/1.87 % (4049883)------------------------------
% 6.26/1.87 % (4049883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.26/1.87 % (4049883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.26/1.87 % (4049883)CaDiCaL version: 2.1.3
% 6.26/1.87 % (4049883)Termination reason: Refutation
% 6.26/1.87 % (4049883)Time elapsed: 0.040 s
% 6.26/1.87 % (4049883)Peak memory usage: 88 MB
% 6.26/1.87 % (4049883)Instructions burned: 39 (million)
% 6.26/1.87 % (4049883)------------------------------
% 6.26/1.87 % (4049883)------------------------------
% 6.26/1.87 % (4049872)Success in time 0.76 s
% 6.26/1.87 % Vampire exiting
%------------------------------------------------------------------------------