%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI535_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:33:18 AM UTC 2026
% Result : Theorem 3.59s 1.29s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 12 ( 1 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 46 ( 0 atm; 12 fun; 24 num; 10 var)
% Number of types : 2 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 0 usr; 1 con; 0-2 aty)
% Number of variables : 10 ( 4 !; 6 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
-1: $int > $int ).
tff(func_def_9,type,
2: $int > $int ).
tff(func_def_10,type,
-2: $int > $int ).
tff(pred_def_1,type,
p: ( $int * $int * $int ) > $o ).
tff(f1,conjecture,
? [X1: $int,X0: $int] :
( p(2,X1,$sum(2,X1))
=> p(X0,2,$product(X0,2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(f2,negated_conjecture,
~ ? [X1: $int,X0: $int] :
( p(2,X1,$sum(2,X1))
=> p(X0,2,$product(X0,2)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f21,plain,
~ ? [X0: $int,X1: $int] :
( p(2,X0,$sum(2,X0))
=> p(X1,2,$product(X1,2)) ),
inference(rectify,[],[f2]) ).
tff(f22,plain,
! [X0: $int,X1: $int] :
( p(2,X0,$sum(2,X0))
& ~ p(X1,2,$product(X1,2)) ),
inference(ennf_transformation,[],[f21]) ).
tff(f23,plain,
! [X1: $int] : ~ p(X1,2,$product(X1,2)),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
! [X0: $int] : p(2,X0,$sum(2,X0)),
inference(cnf_transformation,[],[f22]) ).
tff(f26,plain,
$product(2,2) != $sum(2,2),
inference(constrained_resolution,[],[f24,f23]) ).
tff(f27,plain,
$false,
inference(evaluation,[],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI535_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:56:33 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.59/1.29 % (3991369)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.59/1.29 % (3991459)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2303983118:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.59/1.29 % (3991457)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3311593424:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.59/1.29 % (3991460)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3085754319:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.59/1.29 % (3991463)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2948169850:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.59/1.29 % (3991461)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1072083853:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.59/1.29 % (3991462)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2729525038:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.59/1.29 % (3991461)First to succeed.
% 3.59/1.29 % (3991460)Also succeeded, but the first one will report.
% 3.59/1.29 % (3991461)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3991369"
% 3.59/1.29 % (3991459)Instruction limit reached!
% 3.59/1.29 % (3991459)------------------------------
% 3.59/1.29 % (3991459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991459)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991459)Termination reason: Instruction limit
% 3.59/1.29 % (3991459)Termination phase: Saturation
% 3.59/1.29 % (3991459)Time elapsed: 0.061 s
% 3.59/1.29 % (3991459)Peak memory usage: 113 MB
% 3.59/1.29 % (3991459)Instructions burned: 203 (million)
% 3.59/1.29 % (3991458)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=380233421:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.59/1.29 % (3991462)Refutation not found, incomplete strategy
% 3.59/1.29 % (3991462)------------------------------
% 3.59/1.29 % (3991462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991462)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991462)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.29 % (3991462)Time elapsed: 0.026 s
% 3.59/1.29 % (3991462)Peak memory usage: 112 MB
% 3.59/1.29 % (3991462)Instructions burned: 5 (million)
% 3.59/1.29 % (3991457)Refutation not found, incomplete strategy
% 3.59/1.29 % (3991457)------------------------------
% 3.59/1.29 % (3991457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991457)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991457)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.29 % (3991457)Time elapsed: 0.027 s
% 3.59/1.29 % (3991457)Peak memory usage: 112 MB
% 3.59/1.29 % (3991457)Instructions burned: 5 (million)
% 3.59/1.29 % (3991463)Instruction limit reached!
% 3.59/1.29 % (3991463)------------------------------
% 3.59/1.29 % (3991463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991463)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991463)Termination reason: Instruction limit
% 3.59/1.29 % (3991463)Termination phase: Saturation
% 3.59/1.29 % (3991463)Time elapsed: 0.046 s
% 3.59/1.29 % (3991463)Peak memory usage: 115 MB
% 3.59/1.29 % (3991463)Instructions burned: 34 (million)
% 3.59/1.29 % (3991458)Refutation not found, incomplete strategy
% 3.59/1.29 % (3991458)------------------------------
% 3.59/1.29 % (3991458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991458)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991458)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.29 % (3991458)Time elapsed: 0.036 s
% 3.59/1.29 % (3991458)Peak memory usage: 112 MB
% 3.59/1.29 % (3991458)Instructions burned: 5 (million)
% 3.59/1.29 % (3991509)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2588821420:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.59/1.29 % (3991509)Refutation not found, incomplete strategy
% 3.59/1.29 % (3991509)------------------------------
% 3.59/1.29 % (3991509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991509)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991509)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.29 % (3991509)Time elapsed: 0.0000 s
% 3.59/1.29 % (3991509)Peak memory usage: 88 MB
% 3.59/1.29 % (3991515)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=663896704:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.59/1.29 % (3991515)Instruction limit reached!
% 3.59/1.29 % (3991515)------------------------------
% 3.59/1.29 % (3991515)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991515)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991515)Termination reason: Instruction limit
% 3.59/1.29 % (3991515)Termination phase: Saturation
% 3.59/1.29 % (3991515)Time elapsed: 0.016 s
% 3.59/1.29 % (3991515)Peak memory usage: 88 MB
% 3.59/1.29 % (3991515)Instructions burned: 31 (million)
% 3.59/1.29 % (3991461)Refutation found. Thanks to Tanya!
% 3.59/1.29 % SZS status Theorem for theBenchmark
% 3.59/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.29 % (3991461)------------------------------
% 3.59/1.29 % (3991461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.29 % (3991461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.29 % (3991461)CaDiCaL version: 2.1.3
% 3.59/1.29 % (3991461)Termination reason: Refutation
% 3.59/1.29 % (3991461)Time elapsed: 0.002 s
% 3.59/1.29 % (3991461)Peak memory usage: 89 MB
% 3.59/1.29 % (3991461)Instructions burned: 1 (million)
% 3.59/1.29 % (3991461)------------------------------
% 3.59/1.29 % (3991461)------------------------------
% 3.59/1.29 % (3991369)Success in time 0.436 s
% 3.59/1.29 % Vampire exiting
%------------------------------------------------------------------------------