%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 : Fri Sep 25 02:30:04 PM UTC 2026
% Result : Unsatisfiable 3.42s 1.19s
% Output : CNFRefutation 3.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_comm) ).
fof(f2,axiom,
! [X2,X0,X1] : '+'(X0,'+'(X1,X2)) = '+'('+'(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_assoc) ).
fof(f3,axiom,
! [X0,X1] : times(X0,X1) = times(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_comm) ).
fof(f4,axiom,
! [X2,X0,X1] : times(X0,times(X1,X2)) = times(times(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_assoc) ).
fof(f12,axiom,
! [X0,X1] : times(s(X0),X1) = '+'(X1,times(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_s) ).
fof(f15,axiom,
! [X0] : sum(s(X0)) = '+'(s(X0),sum(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_s) ).
fof(f16,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction_hypothesis) ).
fof(f17,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : '+'(X0,X1) = '+'(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : '+'('+'(X0,X1),X2) = '+'(X0,'+'(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : times(X0,X1) = times(X1,X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : times(times(X0,X1),X2) = times(X0,times(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : '+'(X0,times(X1,X0)) = times(s(X1),X0),
inference(cnf_transformation,[],[f12]) ).
tcf(c_76,plain,
! [X0: $i] : '+'(s(X0),sum(X0)) = sum(s(X0)),
inference(cnf_transformation,[],[f15]) ).
tcf(c_77,plain,
'+'(sum(a),sum(a)) = times(a,s(a)),
inference(cnf_transformation,[],[f16]) ).
tcf(c_78,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
inference(cnf_transformation,[],[f17]) ).
tcf(c_121,plain,
'+'(s(a),'+'(sum(a),'+'(s(a),sum(a)))) != times(s(a),s(s(a))),
inference(demodulation,[status(thm)],[c_78,c_65,c_76]) ).
tcf(c_122,plain,
'+'(s(a),'+'(s(a),'+'(sum(a),sum(a)))) != times(s(a),s(s(a))),
inference(theory_normalisation,[status(thm)],[c_121,c_65,c_64,c_67,c_66]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i] : '+'(X0,times(X1,X0)) = times(X0,s(X1)),
inference(superposition,[status(thm)],[c_74,c_66]) ).
tcf(c_721,plain,
'+'(s(a),'+'(s(a),'+'(sum(a),sum(a)))) != '+'(s(a),times(s(a),s(a))),
inference(demodulation,[status(thm)],[c_122,c_713]) ).
tcf(c_910,plain,
'+'(s(a),'+'(s(a),times(a,s(a)))) != '+'(s(a),times(s(a),s(a))),
inference(demodulation,[status(thm)],[c_721,c_77]) ).
tcf(c_911,plain,
$false,
inference(ground_joinability,[status(thm)],[c_910,c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN134-1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 06:05:04 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running UEQ theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 3.42/1.19 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.42/1.19 % SZS status Started for theBenchmark.p
% 3.42/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.42/1.19
% 3.42/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.42/1.19
% 3.42/1.19 % ------ iProver source info
% 3.42/1.19
% 3.42/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.42/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.42/1.19 % git: non_committed_changes: false
% 3.42/1.19
% 3.42/1.19 % ------ Parsing...% successful
% 3.42/1.19
% 3.42/1.19
% 3.42/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.42/1.19
% 3.42/1.19 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.42/1.19
% 3.42/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.42/1.19
% 3.42/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.42/1.19 % ------ Proving...
% 3.42/1.19 % ------ Problem Properties
% 3.42/1.19
% 3.42/1.19 %
% 3.42/1.19 % clauses 15
% 3.42/1.19 % conjectures 0
% 3.42/1.19 % EPR 0
% 3.42/1.19 % Horn 15
% 3.42/1.19 % unary 15
% 3.42/1.19 % binary 0
% 3.42/1.19 % lits 15
% 3.42/1.19 % lits eq 15
% 3.42/1.19 % fd_pure 0
% 3.42/1.19 % fd_pseudo 0
% 3.42/1.19 % fd_cond 0
% 3.42/1.19 % fd_pseudo_cond 0
% 3.42/1.19 % AC symbols 2
% 3.42/1.19
% 3.42/1.19 % ------ Input Options Time Limit: Unbounded
% 3.42/1.19
% 3.42/1.19
% 3.42/1.19 % ------
% 3.42/1.19 % Current options:
% 3.42/1.19 % ------
% 3.42/1.19
% 3.42/1.19
% 3.42/1.19 %
% 3.42/1.19
% 3.42/1.19 % ------ Proving...
% 3.42/1.19 %
% 3.42/1.19
% 3.42/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.42/1.19
% 3.42/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.42/1.19
% 3.42/1.19
%------------------------------------------------------------------------------