%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO691-1.001 : 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 02:28:48 PM UTC 2026
% Result : Unsatisfiable 5.45s 1.55s
% Output : Refutation 5.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 42 ( 17 unt; 5 def)
% Number of atoms : 93 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 57 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 122 ( 122 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : top(f(f(f(X0,a),X1),f(X2,a)),f(f(X2,f(f(X1,a),a)),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f2,negated_conjecture,
! [X0] : ~ seq(succ(succ(succ(succ(succ(zero))))),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
fof(f3,axiom,
! [X0,X1] :
( ~ top(X0,X1)
| step(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_top) ).
fof(f4,axiom,
! [X2,X0,X1] :
( step(f(X0,X2),f(X1,X2))
| ~ step(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_left) ).
fof(f5,axiom,
! [X2,X0,X1] :
( step(f(X2,X0),f(X2,X1))
| ~ step(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_right) ).
fof(f6,axiom,
! [X0] : seq(zero,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_sequence_zero) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ seq(X0,X1,X2)
| ~ step(X2,X3)
| seq(succ(X0),X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_sequence_succ) ).
fof(f8,definition,
sF0 = succ(zero),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
succ(zero) = sF0,
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
sF1 = succ(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
succ(sF0) = sF1,
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
sF2 = succ(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f13,plain,
succ(sF1) = sF2,
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
sF3 = succ(sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
succ(sF2) = sF3,
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF4 = succ(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f17,plain,
succ(sF3) = sF4,
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0] : ~ seq(sF4,X0,X0),
inference(definition_folding,[],[f2,f17,f15,f13,f11,f9]) ).
fof(f19,plain,
! [X0,X1] :
( ~ step(X0,X1)
| seq(succ(zero),X0,X1) ),
inference(resolution,[],[f6,f7]) ).
fof(f20,plain,
! [X0,X1] :
( seq(sF0,X0,X1)
| ~ step(X0,X1) ),
inference(forward_demodulation,[],[f19,f9]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ step(X0,X1)
| ~ step(X1,X2)
| seq(succ(sF0),X0,X2) ),
inference(resolution,[],[f20,f7]) ).
fof(f22,plain,
! [X2,X0,X1] :
( ~ step(X1,X2)
| ~ step(X0,X1)
| seq(sF1,X0,X2) ),
inference(forward_demodulation,[],[f21,f11]) ).
fof(f23,plain,
! [X2,X0,X1] : step(f(f(f(X0,a),X1),f(X2,a)),f(f(X2,f(f(X1,a),a)),X0)),
inference(resolution,[],[f3,f1]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( ~ step(X0,f(X1,X2))
| seq(sF1,X0,f(X3,X2))
| ~ step(X1,X3) ),
inference(resolution,[],[f22,f4]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( seq(sF1,f(X0,X1),f(X2,X3))
| ~ step(X0,X2)
| ~ step(X1,X3) ),
inference(resolution,[],[f25,f5]) ).
fof(f41,plain,
! [X2,X3,X0,X1,X4] :
( ~ step(X0,X1)
| ~ step(X2,X3)
| ~ step(f(X1,X3),X4)
| seq(succ(sF1),f(X0,X2),X4) ),
inference(resolution,[],[f31,f7]) ).
fof(f42,plain,
! [X2,X3,X0,X1,X4] :
( ~ step(f(X1,X3),X4)
| ~ step(X0,X1)
| ~ step(X2,X3)
| seq(sF2,f(X0,X2),X4) ),
inference(forward_demodulation,[],[f41,f13]) ).
fof(f43,plain,
! [X2,X3,X0,X1,X4] :
( seq(sF2,f(X0,X3),f(f(X4,f(f(X2,a),a)),X1))
| ~ step(X3,f(X4,a))
| ~ step(X0,f(f(X1,a),X2)) ),
inference(resolution,[],[f42,f23]) ).
fof(f46,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ step(X0,f(X1,a))
| ~ step(X2,f(f(X3,a),X4))
| ~ step(f(f(X1,f(f(X4,a),a)),X3),X5)
| seq(succ(sF2),f(X2,X0),X5) ),
inference(resolution,[],[f43,f7]) ).
fof(f47,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ step(f(f(X1,f(f(X4,a),a)),X3),X5)
| ~ step(X0,f(X1,a))
| ~ step(X2,f(f(X3,a),X4))
| seq(sF3,f(X2,X0),X5) ),
inference(forward_demodulation,[],[f46,f15]) ).
fof(f49,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ step(f(X1,f(f(X4,a),a)),X5)
| ~ step(X2,f(f(X3,a),X4))
| seq(sF3,f(X2,X0),f(X5,X3))
| ~ step(X0,f(X1,a)) ),
inference(resolution,[],[f47,f4]) ).
fof(f54,plain,
! [X2,X3,X0,X1,X4,X5] :
( seq(sF3,f(X0,X3),f(f(f(f(X2,a),f(f(X4,a),a)),X5),X1))
| ~ step(X0,f(f(X1,a),X2))
| ~ step(X3,f(f(f(X5,a),X4),a)) ),
inference(resolution,[],[f49,f23]) ).
fof(f57,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ step(X0,f(f(X1,a),X2))
| ~ step(X3,f(f(f(X4,a),X5),a))
| ~ step(f(f(f(f(X2,a),f(f(X5,a),a)),X4),X1),X6)
| seq(succ(sF3),f(X0,X3),X6) ),
inference(resolution,[],[f54,f7]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ step(f(f(f(f(X2,a),f(f(X5,a),a)),X4),X1),X6)
| ~ step(X0,f(f(X1,a),X2))
| ~ step(X3,f(f(f(X4,a),X5),a))
| seq(sF4,f(X0,X3),X6) ),
inference(forward_demodulation,[],[f57,f17]) ).
fof(f59,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ step(f(f(f(X2,a),f(f(X5,a),a)),X4),X6)
| ~ step(X3,f(f(f(X4,a),X5),a))
| seq(sF4,f(X0,X3),f(X6,X1))
| ~ step(X0,f(f(X1,a),X2)) ),
inference(resolution,[],[f58,f4]) ).
fof(f62,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ step(f(f(X6,a),f(f(X2,a),a)),X4)
| seq(sF4,f(X3,X0),f(f(X4,X1),X5))
| ~ step(X3,f(f(X5,a),X6))
| ~ step(X0,f(f(f(X1,a),X2),a)) ),
inference(resolution,[],[f59,f4]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4,X5] :
( seq(sF4,f(X0,X1),f(f(f(f(f(X2,a),f(f(a,a),a)),X3),X4),X5))
| ~ step(X0,f(f(X5,a),f(X3,a)))
| ~ step(X1,f(f(f(X4,a),X2),a)) ),
inference(resolution,[],[f62,f23]) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( ~ step(f(f(f(f(X0,a),f(f(a,a),a)),X1),X2),f(f(X3,a),f(X1,a)))
| ~ step(X3,f(f(f(X2,a),X0),a)) ),
inference(resolution,[],[f64,f18]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ step(f(f(f(X2,a),f(f(a,a),a)),X1),f(X0,a))
| ~ step(X0,f(f(f(f(X1,a),a),X2),a)) ),
inference(resolution,[],[f67,f4]) ).
fof(f72,plain,
! [X0,X1] :
( ~ step(f(f(X1,a),f(f(a,a),a)),X0)
| ~ step(X0,f(f(f(f(a,a),a),X1),a)) ),
inference(resolution,[],[f69,f4]) ).
fof(f74,plain,
! [X0] : ~ step(f(f(f(a,a),f(f(a,a),a)),X0),f(f(f(f(a,a),a),f(X0,a)),a)),
inference(resolution,[],[f72,f23]) ).
fof(f77,plain,
$false,
inference(resolution,[],[f74,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO691-1.001 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 18:08:39 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.61/1.35 % (1005081)Input is clausal, will run a generic CNF schedule.
% 4.61/1.35 % (1005133)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=2838095884:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.61/1.35 % (1005134)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2679266837:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.61/1.35 % (1005136)lrs+10_1_sil=8000:sp=occurrence:random_seed=3795230780:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.61/1.35 % (1005137)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4137440899:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.61/1.35 % (1005135)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2495225581:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.61/1.35 % (1005138)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=567957551:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.61/1.35 % (1005139)dis-21_1_sil=8000:lcm=predicate:random_seed=3258100781: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)
% 4.61/1.35 % (1005137)Refutation not found, incomplete strategy
% 4.61/1.35 % (1005137)------------------------------
% 4.61/1.35 % (1005137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.35 % (1005137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.35 % (1005137)CaDiCaL version: 2.1.3
% 4.61/1.35 % (1005137)Termination reason: Refutation not found, incomplete strategy
% 4.61/1.35 % (1005137)Time elapsed: 0.037 s
% 4.61/1.35 % (1005137)Peak memory usage: 88 MB
% 4.61/1.35 % (1005137)Instructions burned: 63 (million)
% 4.61/1.35 % (1005136)Instruction limit reached!
% 4.61/1.35 % (1005136)------------------------------
% 4.61/1.35 % (1005136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.35 % (1005136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.35 % (1005136)CaDiCaL version: 2.1.3
% 4.61/1.35 % (1005136)Termination reason: Instruction limit
% 4.61/1.35 % (1005136)Termination phase: Saturation
% 4.61/1.35 % (1005136)Time elapsed: 0.069 s
% 4.61/1.35 % (1005136)Peak memory usage: 89 MB
% 4.61/1.35 % (1005136)Instructions burned: 108 (million)
% 4.61/1.35 % (1005139)Instruction limit reached!
% 4.61/1.35 % (1005139)------------------------------
% 4.61/1.35 % (1005139)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.35 % (1005139)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.35 % (1005139)CaDiCaL version: 2.1.3
% 4.61/1.35 % (1005139)Termination reason: Instruction limit
% 4.61/1.35 % (1005139)Termination phase: Saturation
% 4.61/1.35 % (1005139)Time elapsed: 0.067 s
% 4.61/1.35 % (1005139)Peak memory usage: 87 MB
% 4.61/1.35 % (1005139)Instructions burned: 118 (million)
% 4.61/1.35 % (1005138)Instruction limit reached!
% 4.61/1.35 % (1005138)------------------------------
% 4.61/1.35 % (1005138)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.35 % (1005138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.35 % (1005138)CaDiCaL version: 2.1.3
% 4.61/1.35 % (1005138)Termination reason: Instruction limit
% 4.61/1.35 % (1005138)Termination phase: Saturation
% 4.61/1.35 % (1005138)Time elapsed: 0.122 s
% 4.61/1.35 % (1005138)Peak memory usage: 89 MB
% 4.61/1.35 % (1005138)Instructions burned: 181 (million)
% 4.61/1.35 % (1005148)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2815723731:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 4.61/1.35 % (1005147)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=1271567762:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.61/1.35 % (1005148)Refutation not found, incomplete strategy
% 4.61/1.35 % (1005148)------------------------------
% 4.61/1.35 % (1005148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.35 % (1005148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.35 % (1005148)CaDiCaL version: 2.1.3
% 5.45/1.55 % (1005148)Termination reason: Refutation not found, incomplete strategy
% 5.45/1.55 % (1005148)Time elapsed: 0.001 s
% 5.45/1.55 % (1005148)Peak memory usage: 87 MB
% 5.45/1.55 % (1005147)Refutation not found, incomplete strategy
% 5.45/1.55 % (1005147)------------------------------
% 5.45/1.55 % (1005147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.55 % (1005147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.55 % (1005147)CaDiCaL version: 2.1.3
% 5.45/1.55 % (1005147)Termination reason: Refutation not found, incomplete strategy
% 5.45/1.55 % (1005147)Time elapsed: 0.004 s
% 5.45/1.55 % (1005147)Peak memory usage: 88 MB
% 5.45/1.55 % (1005147)Instructions burned: 6 (million)
% 5.45/1.55 % (1005149)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2267218593:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.45/1.55 % (1005137)------------------------------
% 5.45/1.55 % (1005137)------------------------------
% 5.45/1.55 % (1005133)First to succeed.
% 5.45/1.55 % (1005133)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1005081"
% 5.45/1.55 % (1005149)Instruction limit reached!
% 5.45/1.55 % (1005149)------------------------------
% 5.45/1.55 % (1005149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.55 % (1005149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.55 % (1005149)CaDiCaL version: 2.1.3
% 5.45/1.55 % (1005149)Termination reason: Instruction limit
% 5.45/1.55 % (1005149)Termination phase: Saturation
% 5.45/1.55 % (1005149)Time elapsed: 0.139 s
% 5.45/1.55 % (1005149)Peak memory usage: 89 MB
% 5.45/1.55 % (1005149)Instructions burned: 219 (million)
% 5.45/1.55 % (1005153)lrs+10_64_to=lpo:sil=8000:random_seed=3196364740:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 5.45/1.55 % (1005147)------------------------------
% 5.45/1.55 % (1005147)------------------------------
% 5.45/1.55 % (1005148)------------------------------
% 5.45/1.55 % (1005148)------------------------------
% 5.45/1.55 % (1005153)Also succeeded, but the first one will report.
% 5.45/1.55 % (1005133)Refutation found. Thanks to Tanya!
% 5.45/1.55 % SZS status Unsatisfiable for theBenchmark
% 5.45/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.45/1.55 % (1005133)------------------------------
% 5.45/1.55 % (1005133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.45/1.55 % (1005133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.45/1.55 % (1005133)CaDiCaL version: 2.1.3
% 5.45/1.55 % (1005133)Termination reason: Refutation
% 5.45/1.55 % (1005133)Time elapsed: 0.403 s
% 5.45/1.55 % (1005133)Peak memory usage: 128 MB
% 5.45/1.55 % (1005133)Instructions burned: 950 (million)
% 5.45/1.55 % (1005133)------------------------------
% 5.45/1.55 % (1005133)------------------------------
% 5.45/1.55 % (1005081)Success in time 0.674 s
% 5.45/1.55 % Vampire exiting
%------------------------------------------------------------------------------