%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 09:31:18 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.20s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 39 ( 15 unt; 0 def)
% Number of atoms : 70 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 34 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,plain,
c_0 = v_f(c_0),
inference(reorient_equations,[],[f1]) ).
fof(f3,negated_conjecture,
c_less(c_0,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5,negated_conjecture,
! [X0] :
( ~ c_less(c_0,X0,t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X0)),t_a),c_times(X0,c_HOL_Oabs(v_h(v_xa(X0)),t_a),t_a),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f6,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f7,axiom,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| X0 = c_Suc(c_minus(X0,c_1,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
fof(f8,plain,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| c_Suc(c_minus(X0,c_1,tc_nat)) = X0 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] :
( c_less(c_0,X0,tc_nat)
| X0 = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f10,plain,
! [X0] :
( c_less(c_0,X0,tc_nat)
| c_0 = X0 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(c_0,X0) = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f12,plain,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| c_lessequals(c_0,c_times(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f16,axiom,
! [X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f17,axiom,
! [X0] :
( class_LOrder_Ojoin__semilorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f18,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f19,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f20,plain,
~ c_lessequals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a),
inference(resolution,[],[f5,f3]) ).
fof(f21,plain,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[],[f17,f16]) ).
fof(f22,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ),
inference(resolution,[],[f12,f19]) ).
fof(f23,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_HOL_Oabs(X0,X1),X1) ),
inference(resolution,[],[f13,f19]) ).
fof(f24,plain,
c_0 = c_HOL_Oabs(c_0,t_a),
inference(resolution,[],[f22,f6]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X2)
| c_lessequals(X0,X1,X2)
| ~ c_less(X0,X1,X2) ),
inference(resolution,[],[f14,f21]) ).
fof(f26,plain,
! [X0] :
( c_Suc(c_minus(X0,c_1,tc_nat)) = X0
| c_0 = X0 ),
inference(resolution,[],[f8,f10]) ).
fof(f27,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(resolution,[],[f23,f6]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X2,X1)
| c_lessequals(c_0,c_times(X2,X0,X1),X1)
| ~ c_lessequals(c_0,X0,X1) ),
inference(resolution,[],[f15,f18]) ).
fof(f30,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_x,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| c_0 = X0 ),
inference(superposition,[],[f4,f26]) ).
fof(f31,plain,
! [X0,X1] :
( c_lessequals(c_0,c_times(X0,X1,t_a),t_a)
| ~ c_lessequals(c_0,X0,t_a)
| ~ c_lessequals(c_0,X1,t_a) ),
inference(resolution,[],[f28,f6]) ).
fof(f32,plain,
c_0 = v_xa(v_x),
inference(resolution,[],[f30,f20]) ).
fof(f33,plain,
~ c_lessequals(c_HOL_Oabs(v_f(c_0),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(superposition,[],[f20,f32]) ).
fof(f34,plain,
~ c_lessequals(c_HOL_Oabs(c_0,t_a),c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(forward_demodulation,[],[f33,f2]) ).
fof(f35,plain,
~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
inference(forward_demodulation,[],[f34,f24]) ).
fof(f36,plain,
! [X0,X1] :
( ~ c_less(X0,X1,t_a)
| c_lessequals(X0,X1,t_a) ),
inference(resolution,[],[f25,f6]) ).
fof(f37,plain,
c_lessequals(c_0,v_x,t_a),
inference(resolution,[],[f36,f3]) ).
fof(f38,plain,
( ~ c_lessequals(c_0,v_x,t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
inference(resolution,[],[f35,f31]) ).
fof(f39,plain,
~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a),
inference(forward_subsumption_resolution,[],[f38,f37]) ).
fof(f40,plain,
$false,
inference(forward_subsumption_resolution,[],[f39,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.15 % Computer : n012.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Mon Sep 28 20:28:49 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 Running first-order model finding
% 0.09/0.17 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.20 % (3705918)Will run a generic schedule for satisfiability detection.
% 0.09/0.20 % (3705924)% WARNING: option uhcvi not known.
% 0.09/0.20 % (3705927)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2895678332:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.20 % (3705927) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3705918-3705927"...
% 0.09/0.20 % (3705928)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2985440888:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.20 % (3705927)...printing done.
% 0.09/0.20 % (3705924)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=348528562:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.20 % (3705923)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3763774692_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.20 % (3705927)Refutation found. Thanks to Tanya!
% 0.09/0.20 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.20 % (3705927)------------------------------
% 0.09/0.20 % (3705927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.20 % (3705927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.20 % (3705927)CaDiCaL version: 2.1.3
% 0.09/0.20 % (3705927)Termination reason: Refutation
% 0.09/0.20 % (3705927)Time elapsed: 0.002 s
% 0.09/0.20 % (3705927)Peak memory usage: 11 MB
% 0.09/0.20 % (3705927)Instructions burned: 2 (million)
% 0.09/0.20 % (3705918)Success in time 0.02 s
% 0.09/0.20 % Vampire exiting
%------------------------------------------------------------------------------