%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 09:30:58 AM UTC 2026
% Result : Unsatisfiable 2.14s 0.68s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 16 unt; 0 def)
% Number of atoms : 24 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 12 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f2,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_times(X1,X2,X0) = c_times(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_times(X1,c_times(X2,X3,X0),X0) = c_times(X2,c_times(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__3_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f6,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__semigroup__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f7,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(resolution,[],[f6,f2]) ).
fof(f8,plain,
! [X0,X1] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(resolution,[],[f7,f3]) ).
fof(f9,plain,
! [X2,X0,X1] : c_times(X0,c_times(X1,X2,t_b),t_b) = c_times(X1,c_times(X0,X2,t_b),t_b),
inference(resolution,[],[f4,f7]) ).
fof(f10,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(resolution,[],[f5,f2]) ).
fof(f25,plain,
! [X2,X3,X0,X1] : c_times(X1,c_times(X3,c_times(X0,X2,t_b),t_b),t_b) = c_times(X3,c_times(X0,c_times(X1,X2,t_b),t_b),t_b),
inference(superposition,[],[f9,f9]) ).
fof(f32,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(v_ca,c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(superposition,[],[f1,f9]) ).
fof(f34,plain,
! [X2,X0,X1] : c_times(X0,c_times(X1,X2,t_b),t_b) = c_times(c_times(X0,X2,t_b),X1,t_b),
inference(superposition,[],[f8,f9]) ).
fof(f35,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(v_ca,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[],[f32,f8]) ).
fof(f37,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_times(c_HOL_Oabs(v_g(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[],[f35,f25]) ).
fof(f39,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[],[f37,f8]) ).
fof(f41,plain,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[],[f39,f10]) ).
fof(f43,plain,
c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != c_times(v_c,c_times(c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),v_ca,t_b),t_b),
inference(forward_demodulation,[],[f41,f34]) ).
fof(f45,plain,
c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != c_times(v_c,c_times(v_ca,c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[],[f43,f8]) ).
fof(f46,plain,
$false,
inference(trivial_inequality_removal,[],[f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Mon Sep 28 20:32:49 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running first-order theorem proving
% 0.08/0.12 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
% 2.14/0.68 % (3711144)Input is clausal, will run a generic CNF schedule.
% 2.14/0.68 % (3711155)dis-21_1_sil=8000:lcm=predicate:random_seed=364630026: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)
% 2.14/0.68 % (3711152)lrs+10_1_sil=8000:sp=occurrence:random_seed=1647167222:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.14/0.68 % (3711151)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2768762071:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.14/0.68 % (3711154)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=41290893:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.14/0.68 % (3711153)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2380457378:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.14/0.68 % (3711149)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=3296884060:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.14/0.68 % (3711150)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4164317574:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.14/0.68 % (3711155)Refutation not found, incomplete strategy
% 2.14/0.68 % (3711155)------------------------------
% 2.14/0.68 % (3711155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/0.68 % (3711155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.68 % (3711155)CaDiCaL version: 2.1.3
% 2.14/0.68 % (3711155)Termination reason: Refutation not found, incomplete strategy
% 2.14/0.68 % (3711155)Time elapsed: 0.001 s
% 2.14/0.68 % (3711155)Peak memory usage: 88 MB
% 2.14/0.68 % (3711152)First to succeed.
% 2.14/0.68 % (3711152)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3711144"
% 2.14/0.68 % (3711154)Also succeeded, but the first one will report.
% 2.14/0.68 % (3711153)Also succeeded, but the first one will report.
% 2.14/0.68 % (3711155)------------------------------
% 2.14/0.68 % (3711155)------------------------------
% 2.14/0.68 % (3711152)Refutation found. Thanks to Tanya!
% 2.14/0.68 % SZS status Unsatisfiable for theBenchmark
% 2.14/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.14/0.68 % (3711152)------------------------------
% 2.14/0.68 % (3711152)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.14/0.68 % (3711152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.14/0.68 % (3711152)CaDiCaL version: 2.1.3
% 2.14/0.68 % (3711152)Termination reason: Refutation
% 2.14/0.68 % (3711152)Time elapsed: 0.002 s
% 2.14/0.68 % (3711152)Peak memory usage: 88 MB
% 2.14/0.68 % (3711152)Instructions burned: 3 (million)
% 2.14/0.68 % (3711152)------------------------------
% 2.14/0.68 % (3711152)------------------------------
% 2.14/0.68 % (3711144)Success in time 0.277 s
% 2.14/0.68 % Vampire exiting
%------------------------------------------------------------------------------