%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LCL231-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 11:49:26 AM UTC 2026
% Result : Unsatisfiable 97.26s 12.71s
% Output : Proof 97.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL231-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.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 : Sun Sep 27 15:33:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 97.26/12.71 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 97.26/12.71
% 97.26/12.71 % SZS status Unsatisfiable
% 97.26/12.71
% 97.26/12.75 % SZS output start Proof
% 97.26/12.76 Axiom 1 (implies_definition): implies(X, Y) = or(not(X), Y).
% 97.26/12.76 Axiom 2 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 97.26/12.76 Axiom 3 (axiom_1_3): axiom(implies(X, or(Y, X))) = true.
% 97.26/12.76 Axiom 4 (rule_1): ifeq(axiom(X), true, theorem(X), true) = true.
% 97.26/12.76 Axiom 5 (rule_2): ifeq(theorem(implies(X, Y)), true, ifeq(theorem(X), true, theorem(Y), true), true) = true.
% 97.26/12.76 Axiom 6 (axiom_1_6): axiom(implies(implies(X, Y), implies(or(Z, X), or(Z, Y)))) = true.
% 97.26/12.76 Axiom 7 (axiom_1_5): axiom(implies(or(X, or(Y, Z)), or(Y, or(X, Z)))) = true.
% 97.26/12.76
% 97.26/12.76 Goal 1 (prove_this): theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))) = true.
% 97.26/12.76 Proof:
% 97.26/12.76 theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))
% 97.26/12.76 = { by axiom 2 (ifeq_axiom) R->L }
% 97.26/12.76 ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true)
% 97.26/12.76 = { by axiom 2 (ifeq_axiom) R->L }
% 97.26/12.76 ifeq(true, true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 5 (rule_2) R->L }
% 97.26/12.76 ifeq(ifeq(theorem(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))))), true, ifeq(theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 2 (ifeq_axiom) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))))), true), true, ifeq(theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 6 (axiom_1_6) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(or(not(implies(implies(p, q), implies(p, r))), implies(q, implies(p, r))), or(not(implies(implies(p, q), implies(p, r))), implies(p, implies(q, r)))))), true, theorem(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))))), true), true, ifeq(theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 1 (implies_definition) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), or(not(implies(implies(p, q), implies(p, r))), implies(p, implies(q, r)))))), true, theorem(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))))), true), true, ifeq(theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 1 (implies_definition) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))))), true, theorem(implies(implies(implies(q, implies(p, r)), implies(p, implies(q, r))), implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))))), true), true, ifeq(theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 4 (rule_1) }
% 97.26/12.76 ifeq(ifeq(true, true, ifeq(theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 2 (ifeq_axiom) }
% 97.26/12.76 ifeq(ifeq(theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 2 (ifeq_axiom) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(true, true, theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 7 (axiom_1_5) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(or(not(q), or(not(p), r)), or(not(p), or(not(q), r)))), true, theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 1 (implies_definition) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(implies(q, or(not(p), r)), or(not(p), or(not(q), r)))), true, theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 1 (implies_definition) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(implies(q, or(not(p), r)), or(not(p), implies(q, r)))), true, theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 1 (implies_definition) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(p, r)), or(not(p), implies(q, r)))), true, theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 1 (implies_definition) R->L }
% 97.26/12.76 ifeq(ifeq(ifeq(axiom(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true, theorem(implies(implies(q, implies(p, r)), implies(p, implies(q, r)))), true), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.76 = { by axiom 4 (rule_1) }
% 97.26/12.76 ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 2 (ifeq_axiom) }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 5 (rule_2) R->L }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))))), true, ifeq(theorem(implies(q, implies(p, q))), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 2 (ifeq_axiom) R->L }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))))), true, ifeq(ifeq(true, true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 3 (axiom_1_3) R->L }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))))), true, ifeq(ifeq(axiom(implies(q, or(not(p), q))), true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 1 (implies_definition) R->L }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))))), true, ifeq(ifeq(axiom(implies(q, implies(p, q))), true, theorem(implies(q, implies(p, q))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 4 (rule_1) }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))))), true, ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 2 (ifeq_axiom) }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))))), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 1 (implies_definition) }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(implies(q, implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.77 = { by axiom 1 (implies_definition) }
% 97.26/12.77 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 2 (ifeq_axiom) R->L }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(true, true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 4 (rule_1) R->L }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 1 (implies_definition) }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), or(not(or(not(q), implies(p, q))), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 1 (implies_definition) }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), implies(p, r)), or(not(or(not(q), implies(p, q))), or(not(q), implies(p, r)))), or(not(or(not(q), implies(p, q))), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 1 (implies_definition) }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(implies(implies(implies(p, q), implies(p, r)), or(not(or(not(q), implies(p, q))), or(not(q), implies(p, r)))), or(not(or(not(q), implies(p, q))), or(not(implies(implies(p, q), implies(p, r))), or(not(q), implies(p, r)))))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 1 (implies_definition) }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(ifeq(axiom(implies(or(not(implies(implies(p, q), implies(p, r))), or(not(or(not(q), implies(p, q))), or(not(q), implies(p, r)))), or(not(or(not(q), implies(p, q))), or(not(implies(implies(p, q), implies(p, r))), or(not(q), implies(p, r)))))), true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 7 (axiom_1_5) }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(ifeq(true, true, theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 2 (ifeq_axiom) }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 2 (ifeq_axiom) R->L }
% 97.26/12.78 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, ifeq(true, true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.78 = { by axiom 4 (rule_1) R->L }
% 97.26/12.79 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, ifeq(ifeq(axiom(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r))))), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.79 = { by axiom 6 (axiom_1_6) }
% 97.26/12.79 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r))))), true), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.79 = { by axiom 2 (ifeq_axiom) }
% 97.26/12.79 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r)))), implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r)))))), true, ifeq(theorem(implies(implies(implies(p, q), implies(p, r)), implies(or(not(q), implies(p, q)), or(not(q), implies(p, r))))), true, theorem(implies(or(not(q), implies(p, q)), implies(implies(implies(p, q), implies(p, r)), or(not(q), implies(p, r))))), true), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.79 = { by axiom 5 (rule_2) }
% 97.26/12.79 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(ifeq(true, true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.79 = { by axiom 2 (ifeq_axiom) }
% 97.26/12.79 ifeq(theorem(implies(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r))), implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r))))), true, ifeq(theorem(implies(implies(implies(p, q), implies(p, r)), implies(q, implies(p, r)))), true, theorem(implies(implies(implies(p, q), implies(p, r)), implies(p, implies(q, r)))), true), true)
% 97.26/12.79 = { by axiom 5 (rule_2) }
% 97.26/12.79 true
% 97.26/12.79 % SZS output end Proof
% 97.26/12.79
% 97.26/12.79 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------