%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:29:54 PM UTC 2026
% Result : Unsatisfiable 0.88s 1.16s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 21 unt; 0 def)
% Number of atoms : 21 ( 20 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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; 3 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0] : multiply(X0,identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
fof(f6,axiom,
! [X0] : multiply(X0,inverse(X0)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,plain,
! [X0] : identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
tcf(c_55,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_58,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_59,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_60,negated_conjecture,
multiply(inverse(b),inverse(a)) != inverse(multiply(a,b)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_59,c_57]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_57,c_59]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_127,c_55]) ).
tcf(c_143,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_59,c_139]) ).
tcf(c_153,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_143,c_58]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_153,c_139]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(superposition,[status(thm)],[c_132,c_158]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(demodulation,[status(thm)],[c_212,c_58]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_228,c_158]) ).
tcf(c_251,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_60,c_240]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:13:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.39 Running UEQ theorem proving
% 0.09/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 0.88/1.16 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 0.88/1.16 % SZS status Started for theBenchmark.p
% 0.88/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 0.88/1.16
% 0.88/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.88/1.16
% 0.88/1.16 % ------ iProver source info
% 0.88/1.16
% 0.88/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 0.88/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.88/1.16 % git: non_committed_changes: false
% 0.88/1.16
% 0.88/1.16 % ------ Parsing...% successful
% 0.88/1.16
% 0.88/1.16
% 0.88/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.88/1.16
% 0.88/1.16 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.88/1.16
% 0.88/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.88/1.16
% 0.88/1.16 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.88/1.16 % ------ Proving...
% 0.88/1.16 % ------ Problem Properties
% 0.88/1.16
% 0.88/1.16 %
% 0.88/1.16 % clauses 6
% 0.88/1.16 % conjectures 1
% 0.88/1.16 % EPR 0
% 0.88/1.16 % Horn 6
% 0.88/1.16 % unary 6
% 0.88/1.16 % binary 0
% 0.88/1.16 % lits 6
% 0.88/1.16 % lits eq 6
% 0.88/1.16 % fd_pure 0
% 0.88/1.16 % fd_pseudo 0
% 0.88/1.16 % fd_cond 0
% 0.88/1.16 % fd_pseudo_cond 0
% 0.88/1.16 % AC symbols 0
% 0.88/1.16
% 0.88/1.16 % ------ Input Options Time Limit: Unbounded
% 0.88/1.16
% 0.88/1.16
% 0.88/1.16 % ------
% 0.88/1.16 % Current options:
% 0.88/1.16 % ------
% 0.88/1.16
% 0.88/1.16
% 0.88/1.16 %
% 0.88/1.16
% 0.88/1.16 % ------ Proving...
% 0.88/1.16 %
% 0.88/1.16
% 0.88/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 0.88/1.16
% 0.88/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.88/1.16
% 0.88/1.16
%------------------------------------------------------------------------------