%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA035-1 : TPTP v9.3.1. Released v3.2.0.
% 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 09:30:58 AM UTC 2026
% Result : Unsatisfiable 7.85s 1.95s
% Output : Refutation 7.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 27 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 18 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3007,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__semigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f3012,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f3362,axiom,
! [X2,X3,X0,X1] :
( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
fof(f3365,axiom,
! [X2,X3,X0,X1] :
( c_times(X1,c_times(X2,X3,X0),X0) = c_times(X2,c_times(X1,X3,X0),X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__3_0) ).
fof(f3367,axiom,
! [X2,X0,X1] :
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f3376,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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f3377,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3388,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(resolution,[],[f3377,f3007]) ).
fof(f3393,plain,
class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolution,[],[f3377,f3012]) ).
fof(f3506,plain,
( 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) != 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)
| ~ class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(superposition,[],[f3376,f3362]) ).
fof(f3507,plain,
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) != 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_subsumption_resolution,[],[f3506,f3393]) ).
fof(f3745,plain,
( 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) != 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)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(superposition,[],[f3507,f3367]) ).
fof(f3750,plain,
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) != 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_subsumption_resolution,[],[f3745,f3377]) ).
fof(f3839,plain,
( c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),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)
| ~ class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(superposition,[],[f3750,f3362]) ).
fof(f3844,plain,
c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),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_subsumption_resolution,[],[f3839,f3393]) ).
fof(f3898,plain,
( 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) != 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)
| ~ class_OrderedGroup_Oab__semigroup__mult(t_b) ),
inference(superposition,[],[f3844,f3365]) ).
fof(f3899,plain,
~ class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(trivial_inequality_removal,[],[f3898]) ).
fof(f3901,plain,
$false,
inference(forward_subsumption_resolution,[],[f3899,f3388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA035-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 % Computer : n014.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8046.5625MB
% 0.10/0.27 % OS : Linux 6.8.0-71-generic
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 20:33:01 UTC 2026
% 0.26/0.27 % CPUTime :
% 0.26/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running first-order theorem proving
% 0.26/0.32 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
% 7.85/1.95 % (2135370)Input is clausal, will run a generic CNF schedule.
% 7.85/1.95 % (2135388)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2902779515:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.85/1.95 % (2135384)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3233439712:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.85/1.95 % (2135386)lrs+10_1_sil=8000:sp=occurrence:random_seed=885970002:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.85/1.95 % (2135383)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=225891330:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.85/1.95 % (2135385)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1499584350:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.85/1.95 % (2135387)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=959684899:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.85/1.95 % (2135389)dis-21_1_sil=8000:lcm=predicate:random_seed=340998215: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)
% 7.85/1.95 % (2135386)Instruction limit reached!
% 7.85/1.95 % (2135386)------------------------------
% 7.85/1.95 % (2135386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135386)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135386)Termination reason: Instruction limit
% 7.85/1.95 % (2135386)Termination phase: Saturation
% 7.85/1.95 % (2135386)Time elapsed: 0.085 s
% 7.85/1.95 % (2135386)Peak memory usage: 91 MB
% 7.85/1.95 % (2135386)Instructions burned: 107 (million)
% 7.85/1.95 % (2135388)Instruction limit reached!
% 7.85/1.95 % (2135388)------------------------------
% 7.85/1.95 % (2135388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135388)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135388)Termination reason: Instruction limit
% 7.85/1.95 % (2135388)Termination phase: Saturation
% 7.85/1.95 % (2135388)Time elapsed: 0.157 s
% 7.85/1.95 % (2135388)Peak memory usage: 91 MB
% 7.85/1.95 % (2135388)Instructions burned: 180 (million)
% 7.85/1.95 % (2135389)Instruction limit reached!
% 7.85/1.95 % (2135389)------------------------------
% 7.85/1.95 % (2135389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135389)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135389)Termination reason: Instruction limit
% 7.85/1.95 % (2135389)Termination phase: Saturation
% 7.85/1.95 % (2135389)Time elapsed: 0.094 s
% 7.85/1.95 % (2135389)Peak memory usage: 90 MB
% 7.85/1.95 % (2135389)Instructions burned: 118 (million)
% 7.85/1.95 % (2135387)Instruction limit reached!
% 7.85/1.95 % (2135387)------------------------------
% 7.85/1.95 % (2135387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135387)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135387)Termination reason: Instruction limit
% 7.85/1.95 % (2135387)Termination phase: Saturation
% 7.85/1.95 % (2135387)Time elapsed: 0.113 s
% 7.85/1.95 % (2135387)Peak memory usage: 90 MB
% 7.85/1.95 % (2135387)Instructions burned: 114 (million)
% 7.85/1.95 % (2135402)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=239816128:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 7.85/1.95 % (2135404)lrs+10_64_to=lpo:sil=8000:random_seed=674267031:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 7.85/1.95 % (2135401)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=2096897549:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 7.85/1.95 % (2135403)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3868851929:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 7.85/1.95 % (2135401)Refutation not found, incomplete strategy
% 7.85/1.95 % (2135401)------------------------------
% 7.85/1.95 % (2135401)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135401)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135401)Termination reason: Refutation not found, incomplete strategy
% 7.85/1.95 % (2135401)Time elapsed: 0.021 s
% 7.85/1.95 % (2135401)Peak memory usage: 90 MB
% 7.85/1.95 % (2135401)Instructions burned: 18 (million)
% 7.85/1.95 % (2135402)Instruction limit reached!
% 7.85/1.95 % (2135402)------------------------------
% 7.85/1.95 % (2135402)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135402)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135402)Termination reason: Instruction limit
% 7.85/1.95 % (2135402)Termination phase: Saturation
% 7.85/1.95 % (2135402)Time elapsed: 0.104 s
% 7.85/1.95 % (2135402)Peak memory usage: 93 MB
% 7.85/1.95 % (2135402)Instructions burned: 190 (million)
% 7.85/1.95 % (2135404)Instruction limit reached!
% 7.85/1.95 % (2135404)------------------------------
% 7.85/1.95 % (2135404)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135404)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135404)Termination reason: Instruction limit
% 7.85/1.95 % (2135404)Termination phase: Saturation
% 7.85/1.95 % (2135404)Time elapsed: 0.121 s
% 7.85/1.95 % (2135404)Peak memory usage: 92 MB
% 7.85/1.95 % (2135404)Instructions burned: 126 (million)
% 7.85/1.95 % (2135403)First to succeed.
% 7.85/1.95 % (2135403)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2135370"
% 7.85/1.95 % (2135411)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=807979907:avsq=on:i=194:fgj=on:bd=preordered_2993 on theBenchmark for (2993ds/194Mi)
% 7.85/1.95 % (2135412)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=4112416919:i=157:gtg=all_2993 on theBenchmark for (2993ds/157Mi)
% 7.85/1.95 % (2135412)Instruction limit reached!
% 7.85/1.95 % (2135412)------------------------------
% 7.85/1.95 % (2135412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135412)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135412)Termination reason: Instruction limit
% 7.85/1.95 % (2135412)Termination phase: Saturation
% 7.85/1.95 % (2135412)Time elapsed: 0.077 s
% 7.85/1.95 % (2135412)Peak memory usage: 92 MB
% 7.85/1.95 % (2135412)Instructions burned: 157 (million)
% 7.85/1.95 % (2135411)Instruction limit reached!
% 7.85/1.95 % (2135411)------------------------------
% 7.85/1.95 % (2135411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135411)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135411)Termination reason: Instruction limit
% 7.85/1.95 % (2135411)Termination phase: Saturation
% 7.85/1.95 % (2135411)Time elapsed: 0.158 s
% 7.85/1.95 % (2135411)Peak memory usage: 92 MB
% 7.85/1.95 % (2135411)Instructions burned: 195 (million)
% 7.85/1.95 % (2135401)------------------------------
% 7.85/1.95 % (2135401)------------------------------
% 7.85/1.95 % (2135415)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3082102078:i=3394:sd=4:ss=included:sgt=64_2991 on theBenchmark for (2991ds/3394Mi)
% 7.85/1.95 % (2135403)Refutation found. Thanks to Tanya!
% 7.85/1.95 % SZS status Unsatisfiable for theBenchmark
% 7.85/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 7.85/1.95 % (2135403)------------------------------
% 7.85/1.95 % (2135403)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.85/1.95 % (2135403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.85/1.95 % (2135403)CaDiCaL version: 2.1.3
% 7.85/1.95 % (2135403)Termination reason: Refutation
% 7.85/1.95 % (2135403)Time elapsed: 0.081 s
% 7.85/1.95 % (2135403)Peak memory usage: 91 MB
% 7.85/1.95 % (2135403)Instructions burned: 82 (million)
% 7.85/1.95 % (2135403)------------------------------
% 7.85/1.95 % (2135403)------------------------------
% 7.85/1.95 % (2135370)Success in time 1.058 s
% 7.85/1.95 % Vampire exiting
%------------------------------------------------------------------------------