%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 01:00:08 PM UTC 2026
% Result : Unsatisfiable 0.63s 1.09s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 39 unt; 2 def)
% Number of atoms : 85 ( 38 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
fof(f3,axiom,
! [X0,X1] : multiply(X0,X0,X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
fof(f4,axiom,
! [X0,X1] : multiply(inverse(X0),X0,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f5,axiom,
! [X0,X1] : multiply(X0,X1,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_lemma) ).
fof(f6,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f7,plain,
b != multiply(a,inverse(a),b),
inference(reorient_equations,[],[f6]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : multiply(X0,X1,X1) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : multiply(X0,X0,X1) = X0,
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0,X1) = X1,
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : multiply(X0,X1,X0) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,negated_conjecture,
multiply(a,inverse(a),b) != b,
inference(cnf_transformation,[],[f7]) ).
tcf(c_80,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_81,definition,
iPr_def_11 = multiply(a,iPr_def_10,b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_82,negated_conjecture,
iPr_def_11 != b,
inference(demodulation,[status(thm)],[c_60,c_80,c_81]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : multiply(X0,X1,X0) = X0,
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0,X1) = X1,
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : multiply(X0,X0,X1) = X0,
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : multiply(X0,X1,X1) = X1,
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_131,plain,
! [X0: $i] : multiply(iPr_def_10,a,X0) = X0,
inference(superposition,[status(thm)],[c_80,c_84]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] : multiply(a,iPr_def_10,multiply(b,X0,X1)) = multiply(iPr_def_11,X0,multiply(a,iPr_def_10,X1)),
inference(superposition,[status(thm)],[c_81,c_87]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(X0,X1,X2),X3,X1) = multiply(X0,X1,multiply(X2,X3,X1)),
inference(superposition,[status(thm)],[c_86,c_87]) ).
tcf(c_368,plain,
! [X0: $i] : multiply(iPr_def_11,b,multiply(a,iPr_def_10,X0)) = multiply(a,iPr_def_10,b),
inference(superposition,[status(thm)],[c_85,c_140]) ).
tcf(c_614,plain,
! [X0: $i] : multiply(iPr_def_11,b,multiply(a,iPr_def_10,X0)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_368,c_81]) ).
tcf(c_847,plain,
multiply(iPr_def_11,b,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_86,c_614]) ).
tcf(c_848,plain,
multiply(iPr_def_11,b,a) = iPr_def_11,
inference(superposition,[status(thm)],[c_83,c_614]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11,X0,multiply(iPr_def_11,b,X1)) = multiply(iPr_def_11,b,multiply(iPr_def_10,X0,X1)),
inference(superposition,[status(thm)],[c_847,c_87]) ).
tcf(c_1197,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11,X0,multiply(iPr_def_11,b,X1)) = multiply(iPr_def_11,b,multiply(a,X0,X1)),
inference(superposition,[status(thm)],[c_848,c_87]) ).
tcf(c_1558,plain,
! [X0: $i] : multiply(iPr_def_11,a,multiply(iPr_def_11,b,X0)) = multiply(iPr_def_11,b,X0),
inference(superposition,[status(thm)],[c_131,c_1184]) ).
tcf(c_1638,plain,
! [X0: $i] : multiply(iPr_def_11,a,multiply(iPr_def_11,b,X0)) = multiply(iPr_def_11,b,a),
inference(superposition,[status(thm)],[c_85,c_1197]) ).
tcf(c_1682,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(iPr_def_11,X0,multiply(iPr_def_11,b,X1)),X2,b) = multiply(iPr_def_11,b,multiply(multiply(a,X0,X1),X2,b)),
inference(superposition,[status(thm)],[c_1197,c_142]) ).
tcf(c_1757,plain,
! [X0: $i] : multiply(iPr_def_11,a,multiply(iPr_def_11,b,X0)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1638,c_848]) ).
tcf(c_1761,plain,
! [X0: $i] : multiply(iPr_def_11,b,X0) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1558,c_1757]) ).
tcf(c_1806,plain,
! [X0: $i,X1: $i] : multiply(multiply(iPr_def_11,X0,iPr_def_11),X1,b) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1682,c_1761]) ).
tcf(c_1807,plain,
! [X0: $i] : multiply(iPr_def_11,X0,b) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1806,c_83]) ).
tcf(c_2140,plain,
b = iPr_def_11,
inference(superposition,[status(thm)],[c_1807,c_86]) ).
tcf(c_2322,plain,
$false,
inference(superposition,[status(thm)],[c_2140,c_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n002.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 : Fri Sep 25 06:30:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running UEQ theorem proving
% 0.09/0.40 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
% 0.09/0.43 % Proving...
% 0.63/1.09 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 0.63/1.09 % SZS status Started for theBenchmark.p
% 0.63/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 0.63/1.09
% 0.63/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.63/1.09
% 0.63/1.09 % ------ iProver source info
% 0.63/1.09
% 0.63/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 0.63/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.63/1.09 % git: non_committed_changes: false
% 0.63/1.09
% 0.63/1.09 % ------ Parsing...% successful
% 0.63/1.09
% 0.63/1.09
% 0.63/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.63/1.09
% 0.63/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.63/1.09
% 0.63/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.63/1.09
% 0.63/1.09 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.63/1.09 % ------ Proving...
% 0.63/1.09 % ------ Problem Properties
% 0.63/1.09
% 0.63/1.09 %
% 0.63/1.09 % clauses 8
% 0.63/1.09 % conjectures 1
% 0.63/1.09 % EPR 1
% 0.63/1.09 % Horn 8
% 0.63/1.09 % unary 8
% 0.63/1.09 % binary 0
% 0.63/1.09 % lits 8
% 0.63/1.09 % lits eq 8
% 0.63/1.09 % fd_pure 0
% 0.63/1.09 % fd_pseudo 0
% 0.63/1.09 % fd_cond 0
% 0.63/1.09 % fd_pseudo_cond 0
% 0.63/1.09 % AC symbols 0
% 0.63/1.09
% 0.63/1.09 % ------ Input Options Time Limit: Unbounded
% 0.63/1.09
% 0.63/1.09
% 0.63/1.09 % ------
% 0.63/1.09 % Current options:
% 0.63/1.09 % ------
% 0.63/1.09
% 0.63/1.09
% 0.63/1.09 %
% 0.63/1.09
% 0.63/1.09 % ------ Proving...
% 0.63/1.09 %
% 0.63/1.09
% 0.63/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 0.63/1.09
% 0.63/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.63/1.09
% 0.63/1.09
%------------------------------------------------------------------------------