%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP110-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 01:30:55 PM UTC 2026
% Result : Unsatisfiable 2.87s 1.41s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 44 ( 35 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 32 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 9 ( 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 86 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,plain,
( inverse(double_divide(b4,a4)) != inverse(double_divide(a4,b4))
| inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3))
| a2 != inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2)))))
| inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ),
inference(definition_unfolding,[],[f4,f2,f2,f2,f2,f2,f2,f2,f2,f2,f2]) ).
tcf(c_52,negated_conjecture,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,X1)),X2)),double_divide(X0,X2))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(inverse(double_divide(inverse(double_divide(X2,X0)),X3)),X1))) = double_divide(X2,X3),
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,double_divide(inverse(double_divide(X1,X0)),double_divide(X1,X2)))) = X2,
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(double_divide(X0,X1),double_divide(X2,double_divide(inverse(double_divide(inverse(double_divide(X0,X2)),X1)),X3)))) = X3,
inference(superposition,[status(thm)],[c_53,c_115]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),double_divide(X2,X1))) = double_divide(inverse(double_divide(X3,X2)),double_divide(X3,X0)),
inference(superposition,[status(thm)],[c_115,c_53]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,X1)),double_divide(X0,inverse(double_divide(X1,X2)))) = X2,
inference(superposition,[status(thm)],[c_120,c_53]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,inverse(double_divide(inverse(double_divide(X1,X2)),double_divide(X0,X2))))) = X1,
inference(superposition,[status(thm)],[c_120,c_115]) ).
tcf(c_357,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(X0),double_divide(X1,double_divide(X1,inverse(double_divide(X2,X0)))))) = X2,
inference(superposition,[status(thm)],[c_203,c_53]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(inverse(double_divide(X0,X1)),inverse(double_divide(X2,X3))) = inverse(double_divide(double_divide(X0,X2),double_divide(X1,X3))),
inference(superposition,[status(thm)],[c_203,c_118]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(inverse(double_divide(X0,X1)),X2)))) = X2,
inference(superposition,[status(thm)],[c_113,c_115]) ).
tcf(c_1171,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,inverse(X1))),inverse(double_divide(X2,X1))) = double_divide(X0,X2),
inference(superposition,[status(thm)],[c_357,c_637]) ).
tcf(c_1538,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(double_divide(X0,X1),double_divide(inverse(X2),X2))) = double_divide(X0,X1),
inference(demodulation,[status(thm)],[c_1171,c_367]) ).
tcf(c_1541,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,double_divide(inverse(X1),X1))) = X0,
inference(superposition,[status(thm)],[c_203,c_1538]) ).
tcf(c_1607,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(X0,double_divide(inverse(double_divide(X1,X0)),X2))) = double_divide(X1,X2),
inference(superposition,[status(thm)],[c_1541,c_113]) ).
tcf(c_1615,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(X0),inverse(double_divide(X1,X0)))) = X1,
inference(superposition,[status(thm)],[c_1541,c_222]) ).
tcf(c_1620,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_637,c_1607]) ).
tcf(c_1738,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(double_divide(X0,X1)),X2) = double_divide(X0,inverse(double_divide(X1,X2))),
inference(superposition,[status(thm)],[c_203,c_1620]) ).
tcf(c_1744,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(inverse(X0),X1)),double_divide(X2,X1))) = double_divide(X2,X0),
inference(superposition,[status(thm)],[c_1620,c_53]) ).
tcf(c_1759,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(double_divide(inverse(double_divide(X0,double_divide(X0,X1))),X1)),X2)) = X2,
inference(superposition,[status(thm)],[c_1620,c_118]) ).
tcf(c_1765,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(double_divide(X0,X1)),inverse(X1))) = X0,
inference(superposition,[status(thm)],[c_1620,c_222]) ).
tcf(c_1767,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(double_divide(inverse(X0),X0)),X1)) = X1,
inference(light_normalisation,[status(thm)],[c_1759,c_1620]) ).
tcf(c_1776,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(demodulation,[status(thm)],[c_52,c_1738]) ).
tcf(c_1777,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) )
| ( inverse(double_divide(a2,inverse(double_divide(b2,inverse(b2))))) != a2 ) ),
inference(equality_resolution_simp,[status(thm)],[c_1776]) ).
tcf(c_1911,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,inverse(double_divide(X1,inverse(X1))))) = X0,
inference(demodulation,[status(thm)],[c_1765,c_1738]) ).
tcf(c_1912,plain,
( ( a2 != a2 )
| ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ) ),
inference(demodulation,[status(thm)],[c_1777,c_1911]) ).
tcf(c_1913,plain,
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(a1,inverse(a1))) != inverse(double_divide(b1,inverse(b1))) ) ),
inference(equality_resolution_simp,[status(thm)],[c_1912]) ).
tcf(c_1925,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_1911,c_1615]) ).
tcf(c_1926,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,double_divide(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_1911,c_1911]) ).
tcf(c_2026,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,inverse(X1))) = inverse(X0),
inference(superposition,[status(thm)],[c_1926,c_1925]) ).
tcf(c_2078,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(double_divide(inverse(X0),inverse(double_divide(X1,double_divide(X2,X1))))) = double_divide(X2,X0),
inference(demodulation,[status(thm)],[c_1744,c_1738]) ).
tcf(c_2084,plain,
! [X0: $i,X1: $i] : inverse(double_divide(inverse(X0),inverse(X1))) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_1620,c_2078]) ).
tcf(c_2160,plain,
! [X0: $i,X1: $i] : double_divide(X0,inverse(X0)) = double_divide(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_2026,c_1620]) ).
tcf(c_2296,plain,
! [X0: $i] :
( ( inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)) )
| ( inverse(double_divide(X0,inverse(X0))) != inverse(double_divide(a1,inverse(a1))) ) ),
inference(superposition,[status(thm)],[c_2160,c_1913]) ).
tcf(c_2314,plain,
inverse(double_divide(a4,b4)) != inverse(double_divide(b4,a4)),
inference(equality_resolution,[status(thm)],[c_2296]) ).
tcf(c_2315,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = X1,
inference(demodulation,[status(thm)],[c_1767,c_1738,c_2084]) ).
tcf(c_2318,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_1620,c_2315]) ).
tcf(c_2333,plain,
inverse(double_divide(a4,b4)) != inverse(double_divide(a4,b4)),
inference(demodulation,[status(thm)],[c_2314,c_2318]) ).
tcf(c_2337,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP110-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.57 % Computer : n007.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.58 % DateTime : Wed Sep 23 13:31:23 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.58 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.61 Running first-order theorem proving
% 0.14/0.61 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.62
% 0.14/0.62 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.62
% 0.14/0.63 % Detected problem language: tptp
% 0.14/0.64 % Proving...
% 2.87/1.41 % SZS status Started for theBenchmark.p
% 2.87/1.41 % SZS status Unsatisfiable for theBenchmark.p
% 2.87/1.41
% 2.87/1.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.87/1.41
% 2.87/1.41 % ------ iProver source info
% 2.87/1.41
% 2.87/1.41 % git: date: 2026-07-19 20:42:38 +0200
% 2.87/1.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.87/1.41 % git: non_committed_changes: false
% 2.87/1.41
% 2.87/1.41 % ------ Parsing...% successful
% 2.87/1.41
% 2.87/1.41
% 2.87/1.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.87/1.41
% 2.87/1.41 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.87/1.41
% 2.87/1.41 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.87/1.41
% 2.87/1.41 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.87/1.41 % ------ Proving...
% 2.87/1.41 % ------ Problem Properties
% 2.87/1.41
% 2.87/1.41 %
% 2.87/1.41 % clauses 2
% 2.87/1.41 % conjectures 1
% 2.87/1.41 % EPR 0
% 2.87/1.41 % Horn 2
% 2.87/1.41 % unary 1
% 2.87/1.41 % binary 0
% 2.87/1.41 % lits 5
% 2.87/1.41 % lits eq 5
% 2.87/1.41 % fd_pure 0
% 2.87/1.41 % fd_pseudo 0
% 2.87/1.41 % fd_cond 0
% 2.87/1.41 % fd_pseudo_cond 0
% 2.87/1.41 % AC symbols 0
% 2.87/1.41
% 2.87/1.41 % ------ Schedule dynamic 5 is on
% 2.87/1.41
% 2.87/1.41 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.87/1.41
% 2.87/1.41
% 2.87/1.41 % ------
% 2.87/1.41 % Current options:
% 2.87/1.41 % ------
% 2.87/1.41
% 2.87/1.41
% 2.87/1.41 %
% 2.87/1.41
% 2.87/1.41 % ------ Proving...
% 2.87/1.41 %
% 2.87/1.41
% 2.87/1.41 % SZS status Unsatisfiable for theBenchmark.p
% 2.87/1.41
% 2.87/1.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.87/1.41
% 2.87/1.41
%------------------------------------------------------------------------------