%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA030-2 : 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 : n018.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 09:30:56 AM UTC 2026
% Result : Unsatisfiable 3.68s 1.27s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 42 ( 22 unt; 0 def)
% Number of atoms : 67 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 26 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(c_Orderings_Omax(c_minus(v_f(X0),v_g(X0),t_b),c_0,t_b),t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(v_f(v_x(X0)),c_plus(v_g(v_x(X0)),c_times(X0,c_HOL_Oabs(v_h(v_x(X0)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( ~ c_lessequals(c_0,X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X1,c_uminus(X2,X0),X0) = c_minus(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__1_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_minus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_plus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_0) ).
fof(f8,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_plus(X1,X2,X0),X0) = c_plus(c_uminus(X1,X0),c_uminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f9,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_minus(X1,X2,X0),X0) = c_minus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f10,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_uminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f11,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,c_Orderings_Omax(X2,X1,X0),X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Ole__maxI2_0) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Orderings_Omax(X1,X2,X0),X3,X0)
| ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f13,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f14,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(f15,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f16,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f17,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[],[f14,f3]) ).
fof(f18,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(resolution,[],[f15,f3]) ).
fof(f19,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f16,f3]) ).
fof(f20,plain,
! [X0] : c_uminus(c_uminus(X0,t_b),t_b) = X0,
inference(resolution,[],[f10,f18]) ).
fof(f21,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[],[f19,f13]) ).
fof(f22,plain,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Omax(X1,c_0,X0) = c_HOL_Oabs(c_Orderings_Omax(X1,c_0,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(resolution,[],[f4,f11]) ).
fof(f23,plain,
! [X0,X1] : c_plus(X0,c_uminus(X1,t_b),t_b) = c_minus(X0,X1,t_b),
inference(resolution,[],[f5,f18]) ).
fof(f24,plain,
! [X0,X1] : c_minus(X1,c_uminus(X0,t_b),t_b) = c_plus(X1,X0,t_b),
inference(superposition,[],[f23,f20]) ).
fof(f27,plain,
! [X0,X1] : c_minus(X1,X0,t_b) = c_uminus(c_minus(X0,X1,t_b),t_b),
inference(resolution,[],[f9,f18]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_plus(X0,X1,t_b),X2,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(X0,c_plus(X2,c_uminus(X1,t_b),t_b),t_b) ),
inference(superposition,[],[f6,f24]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_plus(X0,X1,t_b),X2,t_b)
| c_lessequals(X0,c_plus(X2,c_uminus(X1,t_b),t_b),t_b) ),
inference(forward_subsumption_resolution,[],[f42,f21]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_plus(X0,X1,t_b),X2,t_b)
| c_lessequals(X0,c_minus(X2,X1,t_b),t_b) ),
inference(forward_demodulation,[],[f43,f23]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_minus(X0,X1,t_b),X2,t_b)
| c_lessequals(X0,c_minus(X2,c_uminus(X1,t_b),t_b),t_b) ),
inference(superposition,[],[f44,f23]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_minus(X0,X1,t_b),X2,t_b)
| c_lessequals(X0,c_plus(X2,X1,t_b),t_b) ),
inference(forward_demodulation,[],[f46,f24]) ).
fof(f49,plain,
! [X0,X1] : c_uminus(c_plus(X0,X1,t_b),t_b) = c_plus(c_uminus(X0,t_b),c_uminus(X1,t_b),t_b),
inference(resolution,[],[f8,f18]) ).
fof(f50,plain,
! [X0,X1] : c_uminus(c_plus(X0,X1,t_b),t_b) = c_minus(c_uminus(X0,t_b),X1,t_b),
inference(forward_demodulation,[],[f49,f23]) ).
fof(f56,plain,
! [X0,X1] : c_plus(X0,X1,t_b) = c_uminus(c_minus(c_uminus(X0,t_b),X1,t_b),t_b),
inference(superposition,[],[f20,f50]) ).
fof(f57,plain,
! [X0,X1] : c_minus(X1,c_uminus(X0,t_b),t_b) = c_plus(X0,X1,t_b),
inference(forward_demodulation,[],[f56,f27]) ).
fof(f73,plain,
! [X0,X1] : c_plus(X1,X0,t_b) = c_plus(X0,X1,t_b),
inference(superposition,[],[f24,f57]) ).
fof(f78,plain,
! [X0] :
( c_Orderings_Omax(X0,c_0,t_b) = c_HOL_Oabs(c_Orderings_Omax(X0,c_0,t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(resolution,[],[f22,f17]) ).
fof(f79,plain,
! [X0] : c_Orderings_Omax(X0,c_0,t_b) = c_HOL_Oabs(c_Orderings_Omax(X0,c_0,t_b),t_b),
inference(forward_subsumption_resolution,[],[f78,f19]) ).
fof(f118,plain,
! [X0] : c_lessequals(c_Orderings_Omax(c_minus(v_f(X0),v_g(X0),t_b),c_0,t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),
inference(superposition,[],[f1,f79]) ).
fof(f732,plain,
! [X0] :
( ~ class_Orderings_Olinorder(t_b)
| c_lessequals(c_minus(v_f(X0),v_g(X0),t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b) ),
inference(resolution,[],[f118,f12]) ).
fof(f733,plain,
! [X0] : c_lessequals(c_minus(v_f(X0),v_g(X0),t_b),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[],[f732,f17]) ).
fof(f735,plain,
! [X0] : c_lessequals(v_f(X0),c_plus(c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),v_g(X0),t_b),t_b),
inference(resolution,[],[f733,f47]) ).
fof(f736,plain,
! [X0] : c_lessequals(v_f(X0),c_plus(v_g(X0),c_times(v_c,c_HOL_Oabs(v_h(X0),t_b),t_b),t_b),t_b),
inference(forward_demodulation,[],[f735,f73]) ).
fof(f1051,plain,
$false,
inference(resolution,[],[f736,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.16 % Computer : n018.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Mon Sep 28 20:34:26 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 3.68/1.27 % (3731841)Input is clausal, will run a generic CNF schedule.
% 3.68/1.27 % (3731850)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1984691169:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.68/1.27 % (3731846)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=1270335804:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.68/1.27 % (3731850)Instruction limit reached!
% 3.68/1.27 % (3731850)------------------------------
% 3.68/1.27 % (3731850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.27 % (3731850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.27 % (3731850)CaDiCaL version: 2.1.3
% 3.68/1.27 % (3731850)Termination reason: Instruction limit
% 3.68/1.27 % (3731850)Termination phase: Saturation
% 3.68/1.27 % (3731850)Time elapsed: 0.033 s
% 3.68/1.27 % (3731850)Peak memory usage: 88 MB
% 3.68/1.27 % (3731850)Instructions burned: 115 (million)
% 3.68/1.27 % (3731851)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=967642930:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.68/1.27 % (3731847)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3486571049:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.68/1.27 % (3731848)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1822582044:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.68/1.27 % (3731849)lrs+10_1_sil=8000:sp=occurrence:random_seed=85759826:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.68/1.27 % (3731852)dis-21_1_sil=8000:lcm=predicate:random_seed=2417078374: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)
% 3.68/1.27 % (3731849)First to succeed.
% 3.68/1.27 % (3731849)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3731841"
% 3.68/1.27 % (3731851)Also succeeded, but the first one will report.
% 3.68/1.27 % (3731852)Instruction limit reached!
% 3.68/1.27 % (3731852)------------------------------
% 3.68/1.27 % (3731852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.27 % (3731852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.27 % (3731852)CaDiCaL version: 2.1.3
% 3.68/1.27 % (3731852)Termination reason: Instruction limit
% 3.68/1.27 % (3731852)Termination phase: Saturation
% 3.68/1.27 % (3731852)Time elapsed: 0.064 s
% 3.68/1.27 % (3731852)Peak memory usage: 89 MB
% 3.68/1.27 % (3731852)Instructions burned: 117 (million)
% 3.68/1.27 % (3731855)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=2248996013:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.68/1.27 % (3731855)Refutation not found, incomplete strategy
% 3.68/1.27 % (3731855)------------------------------
% 3.68/1.27 % (3731855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.27 % (3731855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.27 % (3731855)CaDiCaL version: 2.1.3
% 3.68/1.27 % (3731855)Termination reason: Refutation not found, incomplete strategy
% 3.68/1.27 % (3731855)Time elapsed: 0.001 s
% 3.68/1.27 % (3731855)Peak memory usage: 88 MB
% 3.68/1.27 % (3731855)Instructions burned: 3 (million)
% 3.68/1.27 % (3731861)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1935922184: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)
% 3.68/1.27 % (3731855)------------------------------
% 3.68/1.27 % (3731855)------------------------------
% 3.68/1.27 % (3731861)Also succeeded, but the first one will report.
% 3.68/1.27 % (3731849)Refutation found. Thanks to Tanya!
% 3.68/1.27 % SZS status Unsatisfiable for theBenchmark
% 3.68/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.27 % (3731849)------------------------------
% 3.68/1.27 % (3731849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.27 % (3731849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.27 % (3731849)CaDiCaL version: 2.1.3
% 3.68/1.27 % (3731849)Termination reason: Refutation
% 3.68/1.27 % (3731849)Time elapsed: 0.022 s
% 3.68/1.27 % (3731849)Peak memory usage: 88 MB
% 3.68/1.27 % (3731849)Instructions burned: 32 (million)
% 3.68/1.27 % (3731849)------------------------------
% 3.68/1.27 % (3731849)------------------------------
% 3.68/1.27 % (3731841)Success in time 0.431 s
% 3.68/1.27 % Vampire exiting
%------------------------------------------------------------------------------