%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA023-2 : 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 : n010.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 09:30:54 AM UTC 2026
% Result : Unsatisfiable 3.62s 1.21s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 27 ( 14 unt; 0 def)
% Number of atoms : 46 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,c_minus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_plus(X1,X3,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_minus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f5,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f11,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f12,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f13,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(resolution,[],[f9,f12]) ).
fof(f14,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[],[f10,f12]) ).
fof(f15,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[],[f14,f8]) ).
fof(f16,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[],[f11,f12]) ).
fof(f17,plain,
! [X0] : c_plus(c_0,X0,t_b) = X0,
inference(resolution,[],[f1,f13]) ).
fof(f22,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b) ),
inference(resolution,[],[f2,f5]) ).
fof(f23,plain,
c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),
inference(forward_subsumption_resolution,[],[f22,f16]) ).
fof(f24,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(forward_demodulation,[],[f23,f17]) ).
fof(f25,plain,
! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_g(v_x),X0,t_b) ),
inference(resolution,[],[f24,f4]) ).
fof(f26,plain,
! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| c_lessequals(v_g(v_x),X0,t_b) ),
inference(forward_subsumption_resolution,[],[f25,f15]) ).
fof(f27,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_0,c_minus(X1,X0,t_b),t_b) ),
inference(superposition,[],[f3,f17]) ).
fof(f28,plain,
! [X0,X1] :
( c_lessequals(c_0,c_minus(X1,X0,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(forward_subsumption_resolution,[],[f27,f16]) ).
fof(f29,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[],[f26,f6]) ).
fof(f32,plain,
~ c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(resolution,[],[f28,f7]) ).
fof(f37,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA023-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.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 20:30:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 3.62/1.21 % (2274584)Input is clausal, will run a generic CNF schedule.
% 3.62/1.21 % (2274590)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=698007520:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.62/1.21 % (2274595)dis-21_1_sil=8000:lcm=predicate:random_seed=617324616: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)
% 3.62/1.21 % (2274594)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3344312901:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.62/1.21 % (2274592)lrs+10_1_sil=8000:sp=occurrence:random_seed=888195557:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.62/1.21 % (2274589)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=2275606946:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.62/1.21 % (2274591)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=708409247:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.62/1.21 % (2274593)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1459956339:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.62/1.21 % (2274593)Refutation not found, incomplete strategy
% 3.62/1.21 % (2274593)------------------------------
% 3.62/1.21 % (2274593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.21 % (2274593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.21 % (2274593)CaDiCaL version: 2.1.3
% 3.62/1.21 % (2274593)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.21 % (2274593)Time elapsed: 0.001 s
% 3.62/1.21 % (2274593)Peak memory usage: 87 MB
% 3.62/1.21 % (2274592)First to succeed.
% 3.62/1.21 % (2274595)Also succeeded, but the first one will report.
% 3.62/1.21 % (2274592)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2274584"
% 3.62/1.21 % (2274594)Also succeeded, but the first one will report.
% 3.62/1.21 % (2274593)------------------------------
% 3.62/1.21 % (2274593)------------------------------
% 3.62/1.21 % (2274592)Refutation found. Thanks to Tanya!
% 3.62/1.21 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.21 % (2274592)------------------------------
% 3.62/1.21 % (2274592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.21 % (2274592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.21 % (2274592)CaDiCaL version: 2.1.3
% 3.62/1.21 % (2274592)Termination reason: Refutation
% 3.62/1.21 % (2274592)Time elapsed: 0.002 s
% 3.62/1.21 % (2274592)Peak memory usage: 88 MB
% 3.62/1.21 % (2274592)Instructions burned: 2 (million)
% 3.62/1.21 % (2274592)------------------------------
% 3.62/1.21 % (2274592)------------------------------
% 3.62/1.21 % (2274584)Success in time 0.43 s
% 3.62/1.21 % Vampire exiting
%------------------------------------------------------------------------------